Answer:
The reason for their unusual properties of the greasy feel and low hardness is that the chemical bonds between the sheets is so weak that very low stresses can allow slip between the sheets.
Explanation:
Talc is a monoclinic mineral with a sheet structure similar to the micas and also has perfect cleavage that follows planes between the weakly bonded sheets.
Now, these sheets are held together only by van der Waals bonds and this allows them to slip past each other easily. Thus, this unique characteristic is responsible for talc's extreme softness, its greasy, soapy feel, and its value as a high-temperature lubricant.
While for graphite, it's carbon atoms are linked in a hexagonal network which forms sheets that are one atom thick. It's sheets are poorly connected and easily cleave or slide over one another when subjected to a small amount of force. Thus, gives graphite its very low hardness, its perfect cleavage, and its slippery feel.
So, we can conclude that the reason for their unusual properties is that the chemical bonds between the sheets is so weak that very low stresses can allow slip between the sheets; hence, the greasy feel and low hardness.
A shell-and tube heat exchanger (two shells, four tube passes) is used to heat 10,000 kg/h of pressurized water from 35 to 120 oC with 5000 kg/h pressurized water entering the exchanger at 300 oC. If the overall heat transfer coefficient is 1500 W/m^2-K, determine the required heat exchanger area.
Answer:
4.75m^2
Explanation:
Given:-
- Temperature of hot fluid at inlet: [tex]T_h_i = 300[/tex] °C
- Temperature of cold fluid at outlet: [tex]T_c_o = 120[/tex] °C
- Temperature of cold fluid at inlet: [tex]T_c_i = 35[/tex] °C
- The overall heat transfer coefficient: U = 1500 W / m^2 K
- The flow rate of cold fluid: m_c = 10,00 kg/ h
- The flow rate of hot fluid: m_h = 5,000 kg/h
Solution:-
- We will evaluate water properties at median temperatures of each fluid using table A-4.
Cold fluid: Tci = 35°C , Tco = 35°C
Tcm = 77.5 °C ≈ 350 K --- > [tex]C_p_c = 4195 \frac{J}{kg.K}[/tex]
Hot fluid: Thi = 300°C , Tho = 150°C ( assumed )
Thm = 225 °C ≈ 500 K --- > [tex]C_p_h = 4660 \frac{J}{kg.K}[/tex]
- We will use logarithmic - mean temperature rate equation as follows:
[tex]A_s = \frac{q}{U*dT_l_m}[/tex]
Where,
A_s : The surface area of heat exchange
ΔT_lm: the logarithmic differential mean temperature
q: The rate of heat transfer
- Apply the energy balance on cold fluid as follows:
[tex]q = m_c * C_p_c * ( T_c_o - T_c_i )\\\\q = \frac{10,000}{3600} * 4195 * ( 120 - 35 )\\\\q = 9.905*10^5 W[/tex]
- Similarly, apply the heat balance on hot fluid and evaluate the outlet temperature ( Tho ) :
[tex]T_h_o = T_h_i - \frac{q}{m_h * C_p_h} \\\\T_h_o = 300 - \frac{9.905*10^5}{\frac{5000}{3600} * 4660} \\\\T_h_o = 147 C[/tex]
- We will use the experimental results of counter flow ( unmixed - unmixed ) plotted as figure ( Fig . 11.11 ) of the " The fundamentals to heat transfer" and determine the value of ( P , R , F ).
- So the relations from the figure 11.11 are:
[tex]P = \frac{T_c_o - T_c_i}{T_h_i - T_c_i} \\\\P = \frac{120 - 35}{300 - 35} \\\\P = 0.32[/tex]
[tex]R = \frac{T_h_i - T_h_o}{T_c_o - T_c_i} \\\\R = \frac{300 - 147}{120 - 35} \\\\R = 1.8[/tex]
Therefore, P = 0.32 , R = 1.8 ---- > F ≈ 0.97
- The log-mean temperature ( ΔT_lm - cf ) for counter-flow heat exchange can be determined from the relation:
[tex]dT_l_m = \frac{( T_h_i - T_c_o ) - ( T_h_o - T_c_i ) }{Ln ( \frac{( T_h_i - T_c_o )}{( T_h_o - T_c_i )} ) } \\\\dT_l_m = \frac{( 300 - 120 ) - ( 147 - 35 ) }{Ln ( \frac{( 300-120 )}{( 147-35)} ) } \\\\dT_l_m = 143.3 K[/tex]
- The log - mean differential temperature for counter flow is multiplied by the factor of ( F ) to get the standardized value of log - mean differential temperature:
[tex]dT_l = F*dT_l_m = 0.97*143.3 = 139 K[/tex]
- The required heat exchange area ( A_s ) can now be calculated:
[tex]A_s = \frac{9.905*10^5 }{1500*139} \\\\A_s = 4.75 m^2[/tex]
Liquid benzene and liquid n-hexane are blended to form a stream flowing at a rate of 1700 lbm/h. An on-line densitometer (an instrument used to determine density) indicates that the stream has a density of 0.810 g/mL. Using specific tractors from Table B.1, estimate the mass and volumetric feed rates of the two hydrocarbons to the mixing vessel (in U.S. customary units). State at least two assumptions required to obtain the estimate from the recommended date.
Purely resistive loads of 24 kW, 18 kW, and 12 kW are connected between the neutral
and the red, yellow and blue phases respectively of a 3-0, four-wire system. The line
voltage is 415 V. Calculate:
i. the current in each line conductor (i.e., IR ,Iy and IB); and
ii. the current in the neutral conductor.
Answer:
(i) IR = 100.167 A Iy = 75.125∠-120 IB = 50.083 ∠+120 (ii) IN =43.374∠ -30°
Explanation:
Solution
Given that:
Three loads 24 kW, 18 kW, and 12 kW are connected between the neutral.
Voltage = 415V
Now,
(1)The current in each line conductor
Thus,
The Voltage Vpn = vL√3
Gives us, 415/√3 = 239.6 V
Then,
IR = 24 K/ Vpn ∠0°
24K/239.6 ∠0°= 100.167 A
For Iy
Iy = 18k/239. 6
= 75.125A
Thus,
Iy = 75.125∠-120 this is as a result of the 3- 0 system
Now,
IB = 12K /239.6
= 50.083 A
Thus,
IB is =50.083 ∠+120
(ii) We find the current in the neutral conductor
which is,
IN =Iy +IB +IR
= 75.125∠-120 + 50.083∠+120 +100.167
This will give us the following summation below:
-37.563 - j65.06 - 25.0415 +j 43.373 + 100.167
Thus,
IN = 37.563- j 21.687
Therefore,
IN =43.374∠ -30°
A piston-cylinder assembly contains 5kg of water that undergoes a series of processes to form a thermodynamic cycle. Process 1à 2: Constant pressure cooling from p1=20bar and T1=360°C to saturated vapor Process 2à 3: Constant volume cooling to p3=5 bar Process 3à 4: Constant pressure heating Process 4à 1: Polytropic process following Pv =constant back to the initial state Kinetic and potential energy effects are negligible. Calculate the net work for the cycle in kJ.
Answer:
[tex]W_{net} = - 1223 kJ[/tex]
Explanation:
State 1:
[tex]P_1 = 20 bar\\T_1 = 360^{0}C\\ h_1 = 3159.3 kJ/kg\\S_1 = 6.9917 kJ/kg[/tex]
State 2:
[tex]P_2 = 20 bar\\x_2 = 1 \\ h_2 = 2799.5 kJ/kg\\u_2 = 2600.3 kJ/kg\\v_2 = 0.09963m^3/kg[/tex]
State 3:
[tex]P_2 = 5 bar\\v_2 = v_3 \\v_3 = v_f + x_3 (v_g - v_f)\\0.09963 = (1.0926 * 10^{-3}) +x_3 (0.3749 - (1.0926 * 10^{-3}))\\x_3 = 0.263[/tex]
[tex]u_{3} = u_f + x_3 ( u_g - u_f)\\u_{3} = 639.68 + 0.263 (2561.2 - 639.68)\\u_{3} = 1146.2 kJ/kg[/tex]
State 4:
[tex]P_{4} = 5 bar\\T_4 = 360^0 C\\h_4 = 3188.4 kJ/kg\\S_4 = 7.660 kJ/kg-K\\Q_{12} = h_2 - h_1 = 2799.5-3159.3 = -359 kJ/kg\\Q_{23} = u_3 - h_2 =1146.2-2006.3 = -1454.1 kJ/kg\\Q_{34} = h_4 - h_3 = 3188.4-1196.04 = 1992.36 kJ/kg\\Q_{41} = T(S_1 - S_4) = (360 + 273) (6.9917 - 7.660) = -423.04 kJ/kg[/tex]
Calculate the network done for the cycle
[tex]W_{net} = m( Q_{12} + Q_{23} + Q_{34} + Q_{41})\\W_{net} = 5( -359.8 - 1454.1 + 1992.36 - 423.04)\\W_{net} = -1223 kJ[/tex]
Effluents from metal-finishing plants have the potential of discharging undesirable quantities of metals, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal-finishing plant has identified a wastewater stream that contains 5.15 wt% chromium (Cr) and devised the following approach to lowering risk and recovering the valuable metal. The wastewater stream is fed to a treatment unit that removes 95% of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above 4500 kg/h) bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon.
(a) Without assuming a basis of calculation, draw and label a flowchart of the process. (b) Waste water leaves the finishing plant at a rate m_ 1 ? 6000 kg/h. Calculate the flow rate of liquid to
the waste lagoon, m_ 6?kg/h?, and the mass fraction of Cr in this liquid, x6(kg Cr/kg). (c) Calculate the flow rate of the liquid to the waste lagoon and the mass fraction of Cr in this liquid for m_1 varying from 1000 kg/h to 10,000 kg/h in 1000 kg/h increments. Generate a plot of x6 versus m_ 1 .
(Suggestion: Use a spreadsheet for these calculations.) (d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination? (e) What concerns might need to be addressed regarding the waste lagoon?
Answer:
Explanation:
The solution of all the four parts is provided in the attached figures
g a heat engine is located between thermal reservoirs at 400k and 1600k. the heat engine operates with an efficiency that is 70% of the carnot effieciency. if 2kj of work are produced, how much heat is rejected to the low temperature reservior
Answer:
Heat rejected to cold body = 3.81 kJ
Explanation:
Temperature of hot thermal reservoir Th = 1600 K
Temperature of cold thermal reservoir Tc = 400 K
efficiency of the Carnot's engine = 1 - [tex]\frac{Tc}{Th}[/tex]
eff. of the Carnot's engine = 1 - [tex]\frac{400}{600}[/tex]
eff = 1 - 0.25 = 0.75
efficiency of the heat engine = 70% of 0.75 = 0.525
work done by heat engine = 2 kJ
eff. of heat engine is gotten as = W/Q
where W = work done by heat engine
Q = heat rejected by heat engine to lower temperature reservoir
from the equation, we can derive that
heat rejected Q = W/eff = 2/0.525 = 3.81 kJ
A phone charger requires 0.5 A at 5V. It is connected to a transformer with 100 % of efficiency whose primary contains 2200 turns and is connected to 220-V household outlet.
(a) How many turns should there be in the secondary?
(b) What is the current in the primary?
(c) What would be the output current and output voltage values if number of secondary turns (N2) doubled of its initial value?
Answer:
Explanation:
a ) for transformer which steps down voltage , if V₁ and V₂ be voltage of primary and secondary coil and n₁ and n₂ be the no of turns of wire in them
V₁ /V₂ = n₁ / n₂
Here V₁ = 220 V , V₂ = 5V , n₁ = 2200 n₂ = ?
220 /5 = 2200 / n₂
n₂ = 2200 x 5 / 220
= 50
b )
for 100 % efficiency
input power = output power
V₁ I₁ = V₂I₂
I₁ and I₂ are current in primary and secondary coil
220 x I₁ = 5 x .5
I₁ = .01136 A .
c )
If n₂ = 100
V₁ /V₂ = n₁ / n₂
220 / V₂ = 2200 / 100
V₂ = 10 V
V₁ I₁ = V₂I₂
220 x .01136 = 10 I₂
I₂ = .25 A.
xpress the negative value -22 as a 2's complement integer, using eight bits. Repeat it for 16 bits and 32 bits. What does this illustrate with respect to the properties of sign extension as they pertain to 2's complement representation? 8 bit The 8-bit binary representation of 22 is 00010110. So, -22 in 2’s complement form is (NOT (00010110) + 1) = (11101001 + 1) = 11101010
Answer:
Explanation:
A negative binary number is represeneted by its 2's complement value. To get 2's complement, you just need to invert the bits and add 1 to it. So the formula is:
twos_complement = ~val + 1
So you start out with 22 and you want to make it negative.
22₁₀ = 0001 0110₂
~22₁₀ = 1110 1001₂ inverting the bits
~22₁₀ + 1 = 1110 1010₂ adding 1 to it.
so -22₁₀ == ~22₁₀ + 1 == 1110 1010₂
Do the same process for 16-bits and 32-bits and you'll find that the most significant bits will be padded with 1's.
-22₁₀ = 1110 1010₂ 8-bits
-22₁₀ = 1111 1111 1110 1010₂ 16-bits
-22₁₀ = 1111 1111 1111 1111 1111 1111 1110 1010₂ 32-bits
: Explain why testing can only detect the presence of errors, not their absence?
Answer:
The goal of the software is to observe the software behavior to meet its requirement expectation. In software engineering, validating software might be harder since client's expectation may be vague or unclear.
Explanation:
In contouring, it is necessary to measure position and not velocity for feedback.
a. True
b. False
In contouring during 2-axis NC machining, the two axes are moved at the same speed to achieve the desired contour.
a. True
b. False
Job shop is another term for process layout.
a. True
b. False
Airplanes are normally produced using group technology or cellular layout.
a. True
b. False
In manufacturing, value-creating time is greater than takt time.
a. True
b. False
Answer:
(1). False, (2). True, (3). False, (4). False, (5). True.
Explanation:
The term ''contouring'' in this question does not have to do with makeup but it has to deal with the measurement of all surfaces in planes. It is a measurement in which the rough and the contours are being measured. So, let us check each questions again.
(1). In contouring, it is necessary to measure position and not velocity for feedback.
ANSWER : b =>False. IT IS NECESSARY TO MEASURE BOTH FOR FEEDBACK.
(2). In contouring during 2-axis NC machining, the two axes are moved at the same speed to achieve the desired contour.
ANSWER: a=> True.
(3). Job shop is another term for process layout.
ANSWER: b => False
JOB SHOP IS A FLEXIBLE PROCESS THAT IS BEING USED during manufacturing process and are meant for job Production. PROCESS LAYOUT is used in increasing Efficiency.
(4). Airplanes are normally produced using group technology or cellular layout.
ANSWER: b => False.
(5). In manufacturing, value-creating time is greater than takt time.
ANSWER: a => True.
An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 4 kg of an ideal gas at 750 kPa and 48°C, and the other part is evacuated. The partition is now removed, and the gas expands into the entire tank. Determine the final temperature and pressure in the tank. (Round the final answers to the nearest whole number.)
Answer:
The final temperature and pressure in the insulated rigid tank are [tex]48\,^{\circ}C[/tex] and [tex]375\,kPa[/tex].
Explanation:
An ideal gas is represented by the following model:
[tex]P\cdot V = \frac{m}{M}\cdot R_{u} \cdot T[/tex]
Where:
[tex]P[/tex] - Pressure, measured in kilopascals.
[tex]V[/tex] - Volume, measured in cubic meters.
[tex]m[/tex] - Mass of the ideal gas, measured in kilograms.
[tex]M[/tex] - Molar mass, measured in kilograms per kilomole.
[tex]T[/tex] - Temperature, measured in Kelvin.
[tex]R_{u}[/tex] - Universal constant of ideal gases, equal to [tex]8.314\,\frac{kPa\cdot m^{3}}{kmol\cdot K}[/tex]
As tank is rigid and insulated, it means that no volume deformations in tank, heat and mass interactions with surroundings occur during expansion process. Hence, final pressure is less that initial one, volume is doubled (due to equal partitioning) and temperature remains constant. Hence, the following relationship can be derived from model for ideal gases:
[tex]\frac{P_{1}\cdot V_{1}}{T_{1}} = \frac{P_{2}\cdot V_{2}}{T_{2}}[/tex]
Now, final pressure is cleared:
[tex]P_{2} = P_{1}\cdot \frac{T_{2}}{T_{1}}\cdot \frac{V_{1}}{V_{2}}[/tex]
[tex]P_{2} = (750\,kPa)\cdot 1 \cdot \frac{1}{2}[/tex]
[tex]P_{2} = 375\,kPa[/tex]
The final temperature and pressure in the insulated rigid tank are [tex]48\,^{\circ}C[/tex] and [tex]375\,kPa[/tex].
You are standing at the edge of the roof of the engineering building, which is H meters high. You see Professor Murthy, who is h meters tall, jogging towards the building at a speed of v meters/second. You are holding an egg and want to release it so that it hits Prof Murthy squarely on top of his head. What formulas describes the distance from the building that Prof Murthy must be when you release the egg?
Answer:
s = v√[2(H - h)/g]
This formula describes the distance from the building that Prof Murthy must be when you release the egg
Explanation:
First, we need to find the time required by the egg to reach the head of Professor. For that purpose, we use 1st equation of motion in vertical form:
Vf = Vi + gt
where,
Vf = Velocity of egg at the time of hitting head of the Professor
Vi = initial velocity of egg = 0 m/s (Since, egg is initially at rest)
g = acceleration due to gravity
t = time taken by egg to come down
Therefore,
Vf = 0 + gt
t = Vf/g ----- equation (1)
Now, we use 3rd euation of motion for Vf:
2gs = Vf² - Vi²
where,
s = height dropped = H - h
Therefore,
2g(H - h) = Vf²
Vf = √[2g(H - h)]
Therefore, equation (1) becomes:
t = √[2g(H - h)]/g
t = √[2(H - h)/g]
Now, consider the horizontal motion of professor. So, the minimum distance of professor from building can be found out by finding the distance covered by the professor in time t. Since, the professor is running at constant speed of v m/s. Therefore:
s = vt
s = v√[2(H - h)/g]
This formula describes the distance from the building that Prof Murthy must be when you release the egg
Initially when 1000.00 mL of water at 10oC are poured into a glass cylinder, the height of the water column is 1000.00 mm. The water and its container are heated to 70oC. Assuming no evaporation, what then will be the depth of the water column if the coefficient of thermal expansion for the glass is 3.8*10-6 mm/mm peroC ?
Answer:
[tex]\mathbf{h_2 =1021.9 \ mm}[/tex]
Explanation:
Given that :
The initial volume of water [tex]V_1[/tex] = 1000.00 mL = 1000000 mm³
The initial temperature of the water [tex]T_1[/tex] = 10° C
The height of the water column h = 1000.00 mm
The final temperature of the water [tex]T_2[/tex] = 70° C
The coefficient of thermal expansion for the glass is ∝ = [tex]3.8*10^{-6 } mm/mm \ per ^oC[/tex]
The objective is to determine the the depth of the water column
In order to do that we will need to determine the volume of the water.
We obtain the data for physical properties of water at standard sea level atmospheric from pressure tables; So:
At temperature [tex]T_1 = 10 ^ 0C[/tex] the density of the water is [tex]\rho = 999.7 \ kg/m^3[/tex]
At temperature [tex]T_2 = 70^0 C[/tex] the density of the water is [tex]\rho = 977.8 \ kg/m^3[/tex]
The mass of the water is [tex]\rho V = \rho _1 V_1 = \rho _2 V_2[/tex]
Thus; we can say [tex]\rho _1 V_1 = \rho _2 V_2[/tex];
⇒ [tex]999.7 \ kg/m^3*1000 \ mL = 977.8 \ kg/m^3 *V_2[/tex]
[tex]V_2 = \dfrac{999.7 \ kg/m^3*1000 \ mL}{977.8 \ kg/m^3 }[/tex]
[tex]V_2 = 1022.40 \ mL[/tex]
[tex]v_2 = 1022400 \ mm^3[/tex]
Thus, the volume of the water after heating to a required temperature of [tex]70^0C[/tex] is 1022400 mm³
However; taking an integral look at this process; the volume of the water before heating can be deduced by the relation:
[tex]V_1 = A_1 *h_1[/tex]
The area of the water before heating is:
[tex]A_1 = \dfrac{V_1}{h_1}[/tex]
[tex]A_1 = \dfrac{1000000}{1000}[/tex]
[tex]A_1 = 1000 \ mm^2[/tex]
The area of the heated water is :
[tex]A_2 = A_1 (1 + \Delta t \alpha )^2[/tex]
[tex]A_2 = A_1 (1 + (T_2-T_1) \alpha )^2[/tex]
[tex]A_2 = 1000 (1 + (70-10) 3.8*10^{-6} )^2[/tex]
[tex]A_2 = 1000.5 \ mm^2[/tex]
Finally, the depth of the heated hot water is:
[tex]h_2 = \dfrac{V_2}{A_2}[/tex]
[tex]h_2 = \dfrac{1022400}{1000.5}[/tex]
[tex]\mathbf{h_2 =1021.9 \ mm}[/tex]
Hence the depth of the heated hot water is [tex]\mathbf{h_2 =1021.9 \ mm}[/tex]
In a hydroelectric power plant, water enters the turbine nozzles at 800 kPa absolute with a low velocity. If the nozzle outlets are exposed to atmospheric pressure of 100 kPa, determine the maximum velocity (m/s) to which water can be accelerated by the nozzles before striking the turbine blades.
Answer:
The answer is VN =37.416 m/s
Explanation:
Recall that:
Pressure (atmospheric) = 100 kPa
So. we solve for the maximum velocity (m/s) to which water can be accelerated by the nozzles
Now,
Pabs =Patm + Pgauge = 800 KN/m²
Thus
PT/9.81 + VT²/2g =PN/9.81 + VN²/2g
Here
Acceleration due to gravity = 9.81 m/s
800/9.81 + 0
= 100/9.81 + VN²/19.62
Here,
9.81 * 2= 19.62
Thus,
VN²/19.62 = 700/9.81
So,
VN² =1400
VN =37.416 m/s
Note: (800 - 100) = 700
Answer:
[tex]V2 = 37.417ms^{-1}[/tex]
Explanation:
Given the following data;
Water enters the turbine nozzles (inlet) = 800kPa = 800000pa.
Nozzle outlets = 100kPa = 100000pa.
Density of water = 1000kg/m³.
We would apply, the Bernoulli equation between the inlet and outlet;
[tex]\frac{P_{1} }{d}+\frac{V1^{2} }{2} +gz_{1} = \frac{P_{2} }{d}+\frac{V2^{2} }{2} +gz_{2}[/tex]
Where, V1 is approximately equal to zero(0).
Z[tex]z_{1} = z_{2}[/tex]
Therefore, to find the maximum velocity, V2;
[tex]V2 = \sqrt{2(\frac{P_{1} }{d}-\frac{P_{2} }{d}) }[/tex]
[tex]V2 = \sqrt{2(\frac{800000}{1000}-\frac{100000}{1000}) }[/tex]
[tex]V2 = \sqrt{2(800-100)}[/tex]
[tex]V2 = \sqrt{2(700)}[/tex]
[tex]V2 = \sqrt{1400}[/tex]
[tex]V2 = 37.417ms^{-1}[/tex]
Hence, the maximum velocity, V2 is 37.417m/s
A float valve, regulating the flow of water into a reservoir, is shown in the figure. The spherical float (half of the sphere is submerged) is 0.1553 m in diameter. AOB is the weightless link carrying the float at one end, and a valve at the other end which closes the pipe through which flows into the reservoir. The link is mounted on a frictionless hinge at O, and the angle AOB is 135o. The length of OA is 253 mm and the distance between the center of the float and the hinge is 553 mm. When the flow is stopped AO will be vertical. The valve is to be pressed on to the seat with a force of 10,53 N to be completely stop the flow in the reservoir. It was observed that the flow of water is stopped, when the free surface of water in the reservoir is 353 mm below the hinge at O. Determine the weight of the float sphere.
Answer:
9.29 N . . . . weight of 0.948 kg sphere
Explanation:
The sum of torques on the link BOA is zero, so we have ...
(right force at A)(OA) = (up force at B)(OB·sin(135°))
Solving for the force at B, we have ...
up force at B = (10.53 N)(253 mm)/((553 mm)/√2) ≈ 6.81301 N
This force is due to the difference between the buoyant force on the float sphere and the weight of the float sphere. Dividing by the acceleration due to gravity, it translates to the difference in mass between the water displaced and the mass of the sphere.
∆mass = (6.81301 N)/(9.8 m/s^2) = 0.695205 kg
__
The center of the sphere of diameter 0.1553 m is below the waterline by ...
(553 mm)cos(45°) -(353 mm) = 38.0300 mm
The volume of the spherical cap of radius 155.3/2 = 77.65 mm and height 77.65+38.0300 = 115.680 mm can be found from the formula ...
V = (π/3)h^3(3r -h) = (π/3)(115.680^2)(3·77.65 -115.68) mm^3 ≈ 1.64336 L
So the mass of water contributing to the buoyant force is 1.64336 kg. For the net upward force to correspond to a mass of 0.695305 kg, the mass of the float sphere must be ...
1.64336 kg -0.695205 kg ≈ 0.948 kg
The weight of the float sphere is then (9.8 m/s^2)·(0.948 kg) = 9.29 N
The weight of the 0.948 kg float sphere is about 9.29 N.
A small grinding wheel is attached to the shaft of an electric motor which has a rated speed of 4200 rpm. When the power is turned on, the unit reaches its rated speed in 5 s, and when the power is turned off, the unit coasts to rest in 70 s. Assume uniformly accelerated motion. determine the number of revolutions that the motor executes
(a) in reaching its rated speed,
(b) in coating to rest.
Answer:
a) [tex]\ddot n = 50400\,\frac{rev}{min^{2}}[/tex], b) [tex]n = 2450\,rev[/tex]
Explanation:
a) The acceleration experimented by the grinding wheel is:
[tex]\ddot n = \frac{4200\,\frac{rev}{min} - 0 \,\frac{rev}{min} }{\frac{5}{60}\,min }[/tex]
[tex]\ddot n = 50400\,\frac{rev}{min^{2}}[/tex]
Now, the number of revolutions done by the grinding wheel in that period of time is:
[tex]n = \frac{(4200\,\frac{rev}{min} )^{2}-(0\,\frac{rev}{min} )^{2}}{2\cdot \left(50400\,\frac{rev}{min^{2}} \right)}[/tex]
[tex]n = 175\,rev[/tex]
b) The acceleration experimented by the grinding wheel is:
[tex]\ddot n = \frac{0 \,\frac{rev}{min} - 4200\,\frac{rev}{min} }{\frac{70}{60}\,min }[/tex]
[tex]\ddot n = -3600\,\frac{rev}{min^{2}}[/tex]
Now, the number of revolutions done by the grinding wheel in that period of time is:
[tex]n = \frac{(0\,\frac{rev}{min} )^{2} - (4200\,\frac{rev}{min} )^{2}}{2\cdot \left(-3600\,\frac{rev}{min^{2}} \right)}[/tex]
[tex]n = 2450\,rev[/tex]
A rectangular bar of length L has a slot in the central half of its length. The bar has width b, thickness t, and elastic modulus E. The slot has width b/3. The overall length of the bar is L = 570 mm, and the elastic modulus of the material is 77 GPa. If the average normal stress in the central portion of the bar is 200 MPa, calculate the overall elongation δ of the bar.
Answer:
The correct answer to the following question will be "1.23 mm".
Explanation:
The given values are:
Average normal stress,
[tex]\sigma=200 \ MPa[/tex]
Elastic module,
[tex]E = 77 \ GPa[/tex]
Length,
[tex]L = 570 \ mm[/tex]
To find the deformation, firstly we have to find the equation:
⇒ [tex]\delta=\Sigma\frac{N_{i}L_{i}}{E \ A_{i}}[/tex]
⇒ [tex]=\frac{P(\frac{L}{H})}{E(bt)} +\frac{P(\frac{L}{2})}{E (bt)(\frac{2}{3})}+\frac{P(\frac{L}{H})}{Ebt}[/tex]
On taking "[tex]\frac{PL}{Ebt}[/tex]" as common, we get
⇒ [tex]=\frac{\frac{PL}{Ebt}}{[\frac{1}{4}+\frac{3}{4}+\frac{1}{4}]}[/tex]
⇒ [tex]=\frac{5PL}{HEbt}[/tex]
Now,
The stress at the middle will be:
⇒ [tex]\sigma=\frac{P}{A}[/tex]
⇒ [tex]=\frac{P}{(\frac{2}{3})bt}[/tex]
⇒ [tex]=\frac{3P}{2bt}[/tex]
⇒ [tex]\frac{P}{bt} =\frac{2 \sigma}{3}[/tex]
Hence,
⇒ [tex]\delta=\frac{5 \sigma \ L}{6E}[/tex]
On putting the estimated values, we get
⇒ [tex]=\frac{5\times 200\times 570}{6\times 77\times 10^3}[/tex]
⇒ [tex]=\frac{570000}{462000}[/tex]
⇒ [tex]=1.23 \ mm[/tex]
Consider a classroom for 56 students and one instructor, each generating heat at a rate of 100 W. Lighting is provided by 18 fluorescent lightbulbs, 40 W each, and the ballasts consume an additional 10 percent. Determine the rate of internal heat generation in this classroom when it is fully occupied. The rate of internal heat generation in this classroom when it is fully occupied is W.
Answer:
What is the probability of selecting the 4 of spade or black diamond from a deck of 52 playing cards?
a) 2/52
b) 4/52
c) 3/52
d) 1/5
Explanation:
Increase the sampling time by a factor of 10 (to 0.1 seconds), keeping the frequency of the square wave the same, and observe the delay. Discuss relationship between sampling time and delay from one board to another.
Answer:
Time delay increases
Explanation:
Time delay is the delay between occurance of signal. If sampling time that is time between two samples is increased, the delay in the occurance of regenerated samples is also increased.
two opposite poles repel each other
Answer:
South Pole and South Pole or North Pole and North Pole.
For the pipe-fl ow-reducing section of Fig. P3.54, D 1 5 8 cm, D 2 5 5 cm, and p 2 5 1 atm. All fl uids are at 20 8 C. If V 1 5 5 m/s and the manometer reading is h 5 58 cm, estimate the total force resisted by the fl ange bolts.
Answer:
The total force resisted by the flange bolts is 163.98 N
Explanation:
Solution
The first step is to find the pipe cross section at the inlet section
Now,
A₁ = π /4 D₁²
D₁ = diameter of the pipe at the inlet section
Now we insert 8 cm for D₁ which gives us A₁ = π /4 D (8)²
=50.265 cm² * ( 1 m²/100² cm²)
= 5.0265 * 10^⁻³ m²
Secondly, we find cross section area of the pipe at the inlet section
A₂ = π /4 D₂²
D₂ = diameter of the pipe at the inlet section
Now we insert 5 cm for D₁ which gives us A₁ = π /4 D (5)²
= 19.63 cm² * ( 1 m²/100² cm²)
= 1.963 * 10^⁻³ m²
Now,
we write down the conversation mass relation which is stated as follows:
Q₁ = Q₂
Where Q₁ and Q₂ are both the flow rate at the exist and inlet.
We now insert A₁V₁ for Q₁ and A₂V₂ for Q₂
So,
V₁ and V₂ are defined as the velocities at the inlet and exit
We now insert 5.0265 * 10^⁻³ m² for A₁ 5 m/s for V₁ and 1.963 * 10^⁻³ m² for A₂
= 5.0265 * 5 = 1.963 * V₂
V₂ = 12.8 m/s
Note: Kindly find an attached copy of the part of the solution to the given question below
list everything wrong with 2020
Answer:
George Floyd (BLACK LIFES MATTER)
C O V I D - 19
Quarantine
no sports
wearing a mask
and a whole lot of other stuff
Explanation:
The drum has a mass of 50 kg and a radius of gyration about the pin at O of 0.23 o k m = . If the 15kg block is moving downward at 3 / m s , and a force of P N =100 is applied to the brake arm, determine how far the block descends from the instant the brake is applied until it stops. Neglect the thickness of the handle. The coefficient of kinetic friction at the brake pad is 0.5 k = .
Note: The diagram referred to in this question is attached as a file below.
Answer:
The block descended a distance of 9.75m from the instant the brake is applied until it stops.
Explanation:
For clarity and easiness of expression, the calculations and the Free Body Diagram are contained in the attached file. Check the attached file below.
The block descended a distance of 9.75 m
When an electrical signal travels through a conductive wire, it produces an electromagnetic (EM) field. Likewise, when an EM field encounters a conductive wire, it produces a proportional electrical current.
A. True
B. False
Answer:
A. True
Explanation:
When an electromagnetic field wave strikes a conductor, say a wire, it induces an alternating current that is proportional to the wave in the conductor. This is a reversal of generating electromagnetic wave from accelerating a charged particle. This phenomenon is used in radio antena for receiving radio wave signals and also use in medicine for body scanning.
Under the normal sign convention, the distributed load on a beam is equal to the:_______A. The rate of change of the bending moment with respect to the shear force. B. The second derivative of the bending moment with respect to the length of the beam. C. The rate of change of the bending moment with respect to the length of the beam. D. Negative of the rate of change of the shear force with respect to the length of the beam.
Answer:
Under the normal sign convention, the distributed load on a beam is equal to the: O The second derivative of the bending moment with respect to the length of the beam O Negative of the rate of change of the shear force with respect to the length of the beam.
Sorry if the answer is wrong
Water vapor initially at 3.0 MPa and 300°C (state 1) is contained within a piston- cylinder. The water is cooled at constant volume until its temperature is 200°C (state 2). The water is then compressed isothermally to a state where the pressure is 2.5 MPa (state 3).a. Locate states 1, 2, and 3 on a T-v and P-v diagram.b. Determine the specific volume at all three states.c. Calculate the compressibility factor Z at state 1 and comment.d. Find the quality (if applicable) at all three states.
Answer:
a. T-V and P-V diagram are included
b. State 1: Specific volume = 0.0811753 m³/kg
State 2: Specific volume = 0.0811753 m³/kg
State 3: Specific volume = 0.0804155 m³/kg
c. Z = 51.1
d. Quality for state 1 = 100%
Quality for state 2 = 63.47%
Quality for state 3 = 100%
Explanation:
a. T-V and P-V diagram are included
b. State 1: Water vapor
P₁ = 3.0 MPa = 30 bar
T₁ = 300°C = 573.15
Saturation temperature = 233.86°C Hence the steam is super heated
Specific volume = 0.0811753 m³/kg
State 2:
Constant volume formula is P₁/T₁ = P₂/T₂
Specific volume = 0.0811753 m³/kg
T₂ = 200°C = 473.15
Therefore, P₂ = P₁/T₁ × T₂ = 3×473.15/573.15 = 2.4766 MPa
At T₂ water is mixed water and steam and the [tex]v_f[/tex] = 0.00115651 m³/kg
[tex]v_g[/tex] = 0.127222 m³/kg
State 3:
P₃ = 2.5 MPa
T₃ = 200°C
Isothermal compression P₂V₂ = P₃V₃
V₃ = P₂V₂ ÷ P₃ = 2.4766 × 0.0811753/2.5 = 0.0804155 m³/kg
Specific volume = 0.0804155 m³/kg
2) Compressibility factor is given by the relation;
[tex]Z = \dfrac{PV}{RT} = \dfrac{3\times 10^6 \times 0.0811753 }{8.3145 \times 573.15} = 51.1[/tex]
Z = 51.1
3) Gas quality, x, is given by the relation
[tex]x = \dfrac{Mass_{saturated \, vapor}}{Total \, mass} = \dfrac{v - v_f}{v_g - v_f}[/tex]
Quality at state 1 = Saturated quality = 100%
State 2 Vapor + liquid Quality
Gas quality = (0.0811753 - 0.00115651)/ (0.127222-0.00115651) = 63.47%
State 3: Saturated vapor, quality = 100%.
Suppose you used the pipette to make 10 additions to a flask, and suppose the pipette had a 10% random error in the amount delivered with each delivery. Use equation 1 on page 25 to calculate the percent error in the total volume delivered to the flask using the number of clicks you were permitted to make. Report that total percentage below.
Here is the equation: random error of average= error in one measurement/n^1/2
Answer:
The total percentage is 3.16237%
Explanation:
Solution
Now,
We have to know what a random error is.
A random error is an error in measured caused by factors or elements which varies from one measurement to another.
The random error is shown as follows:
The average random error is = the error found in one measurement/n^1/2
Where
n =Number ( how many times the experiment was done)
Now that we added 10 times we have that,
n → 10
Thus,
The error in one measurement = 10%
So,
The average random error = 10 %/(10)^1/2
= (10)^1/2 %
√10%
The total percentage is = 3.16237%
there is usually a positive side and a negative side to each new technological improvement?
Answer:
positive sides:
low cost improves production speedless timeeducational improvementsnegative sides:
unemployment lot of space required increased pollution creates lots of ethical issuesThe internal loadings at a critical section along the steel drive shaft of a ship are calculated to be a torque of 2300 lb⋅ft, a bending moment of 1500 lb⋅ft, and an axial thrust of 2500 lb. If the yield points for tension and shear are σY= 100 ksi and τY = 50 ksi, respectively, determine the required diameter of the shaft using the maximum-shear-stress theory
Answer:
Explanation:
Given that:
Torque T = 2300 lb - ft
Bending moment M = 1500 lb - ft
axial thrust P = 2500 lb
yield points for tension σY= 100 ksi
yield points for shear τY = 50 ksi
Using maximum-shear-stress theory
[tex]\sigma_A = \dfrac{P}{A}+\dfrac{Mc}{I}[/tex]
where;
[tex]A = \pi c^2[/tex]
[tex]I = \dfrac{\pi}{4}c^4[/tex]
[tex]\sigma_A = \dfrac{P}{\pi c^2}+\dfrac{Mc}{ \dfrac{\pi}{4}c^4}[/tex]
[tex]\sigma_A = \dfrac{2500}{\pi c^2}+\dfrac{1500*12c}{ \dfrac{\pi}{4}c^4}[/tex]
[tex]\sigma_A = \dfrac{2500}{\pi c^2}+\dfrac{72000c}{\pi c^3}}[/tex]
[tex]\tau_A = \dfrac{T_c}{\tau}[/tex]
where;
[tex]\tau = \dfrac{\pi c^4}{2}[/tex]
[tex]\tau_A = \dfrac{T_c}{\dfrac{\pi c^4}{2}}[/tex]
[tex]\tau_A = \dfrac{2300*12 c}{\dfrac{\pi c^4}{2}}[/tex]
[tex]\tau_A = \dfrac{55200 }{\pi c^3}}[/tex]
[tex]\sigma_{1,2} = \dfrac{\sigma_x+\sigma_y}{2} \pm \sqrt{\dfrac{(\sigma_x - \sigma_y)^2}{2}+ \tau_y^2}[/tex]
[tex]\sigma_{1,2} = \dfrac{2500+72000}{2 \pi c ^3} \pm \sqrt{\dfrac{(2500 +72000)^2}{2 \pi c^3}+ \dfrac{55200}{\pi c^3}} \ \ \ \ \ ------(1)[/tex]
Let say :
[tex]|\sigma_1 - \sigma_2| = \sigma_y[/tex]
Then :
[tex]2\sqrt{( \dfrac{2500c + 72000}{2 \pi c^3})^2+ ( \dfrac{55200}{\pi c^3})^2 } = 100(10^3)[/tex]
[tex](2500 c + 72000)^2 +(110400)^2 = 10000*10^6 \pi^2 c^6[/tex]
[tex]6.25c^2 + 360c+ 17372.16-10,000\ \pi^2 c^6 =0[/tex]
According to trial and error;
c = 0.75057 in
Replacing c into equation (1)
[tex]\sigma_{1,2} = \dfrac{2500+72000}{2 \pi (0.75057) ^3} \pm \sqrt{\dfrac{(2500 +72000)^2}{2 \pi (0.75057)^3}+ \dfrac{55200}{\pi (0.75057)^3}}[/tex]
[tex]\sigma_{1,2} = \dfrac{2500+72000}{2 \pi (0.75057) ^3} + \sqrt{\dfrac{(2500 +72000)^2}{2 \pi (0.75057)^3}+ \dfrac{55200}{\pi (0.75057)^3}} \ \ \ OR \\ \\ \\ \sigma_{1,2} = \dfrac{2500+72000}{2 \pi (0.75057) ^3} - \sqrt{\dfrac{(2500 +72000)^2}{2 \pi (0.75057)^3}+ \dfrac{55200}{\pi (0.75057)^3}}[/tex]
[tex]\sigma _1 = 22193 \ Psi[/tex]
[tex]\sigma_2 = -77807 \ Psi[/tex]
The required diameter d = 2c
d = 1.50 in or 0.125 ft
An aluminium bar 600mm long with a diameter 40mm has a hole drilled in the centre of which 30mm in diameter and 100mm long if the modulus of elasticity is 85GN/M2 calculate the total contraction oon the bar due to comprehensive load of 160KN.
Answer:
Total contraction on the bar = 1.238 mm
Explanation:
Modulus of Elasticity, E = 85 GN/m²
Diameter of the aluminium bar, [tex]d_{Al} = 40 mm = 0.04 m[/tex]
Load, P = 160 kN
Cross sectional area of the aluminium bar without hole:
[tex]A_1 = \frac{\pi d_{Al}^2 }{4} \\A_1 = \frac{\pi 0.04^2 }{4}\\A_1 = 0.00126 m^2[/tex]
Diameter of hole, [tex]d_h = 30 mm = 0.03 m[/tex]
Cross sectional area of the aluminium bar with hole:
[tex]A_2 = \frac{\pi( d_{Al}^2 - d_{h}^2)}{4} \\A_2 = \frac{\pi (0.04^2 - 0.03^2) }{4}\\A_2 = 0.00055 m^2[/tex]
Length of the aluminium bar, [tex]L_{Al} = 600 mm = 0.6 m[/tex]
Length of the hole, [tex]L_h = 100mm = 0.1 m[/tex]
Contraction in aluminium bar without hole [tex]= \frac{P * L_{Al}}{A_1 E}[/tex]
Contraction in aluminium bar without hole [tex]= \frac{160*10^3 * 0.6}{0.00126 * 85 * 10^9 }[/tex]
Contraction in aluminium bar without hole = 96000/107100000
Contraction in aluminium bar without hole = 0.000896
Contraction in aluminium bar with hole [tex]= \frac{P * L_{h}}{A_2 E}[/tex]
Contraction in aluminium bar without hole [tex]= \frac{160*10^3 * 0.1}{0.00055 * 85 * 10^9 }[/tex]
Contraction in aluminium bar without hole = 16000/46750000
Contraction in aluminium bar without hole = 0.000342
Total contraction = 0.000896 + 0.000342
Total contraction = 0.001238 m = 1.238 mm
