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MAE 320 HW 1 Assignment Due on Friday, January 23, 2015

(1). Multiple choice (25 points) (1a). (5p) If the units of a quantity x are )/( skgkJ and the units of t are s, what are the units of q in the equation below?

(A) kJ (B) kJ/kg (C) )/( skgkJ (D) kW (1b). (5p) In order for a system to be in thermal equilibrium, which of the following properties must be the same throughout the system (A) mass (B) pressure (C) temperature (D) density (1c). (5p) A specific property is also (A) an extensive property (B) the product of two extensive properties (C) an amount of mass dependent property (D) an intensive property (1d). (5p) The atmospheric pressures at the top and the bottom of a building are read by a barometer to be 0.96 and 0.98 bar. If the density of air is 1.0 kg/m3, the height of the building is (A) 17 m (B) 252 m (C) 170 m (D) 204 m (1e). (5p) For a control volume (or an open) system, (A) The volume of an open system must be constant with prolonging of time (B) Both mass and energy can across the boundary of a control volume. (C) The amount of mass is fixed, but energy can transfer in or out of the system. (D) The boundary of system is fixed (can not be moved). (1f). During a heating process, the temperature of an object rises by 20C. This temperature rise is equivalent to a temperature rise of (A) 20F (B) 52F

1 2 3 4 5 6 7 8

25

10

10

10

10

15

15

5

100

2

(C) 36 K (D) 36 R (E) 293 K 2. Simple calculation question (10 points). 2a. Please demonstrate the unit of VP is Joule, where units of P and V is Pa and m3, respectively. Solution to problem 2a: 2b. The mass of air in a room 3520 m is 350 kg. Determine the density, specific volume, and specific weight of the air Solution to problem 2b: The density is given by

3/167.12053

350 mkgmmm

kgVm

=

==

The specific volume is the inverse density, hence it is given by

kgmmkg

/857.0/167.1

11 33 ===

Finally, the specific weight is

323 /45.11)/81.9)(/167.1( mNsmmkgg === g

J = N m = Pa m2 m = Pa m

3

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3. As shown in the figure, a cylinder of compacted scrap metal with height of L=2 m and diameter of 0.5 m is suspended from a spring scale at a location where the acceleration of gravity is 9.78 m/s2. If the scrap metal density, in kg/m3, varies with the position z according to the law =7800 360(z/L)2, please determine the reading of the scale, in N. (10 points) Solution to problem 3:

4

4. Determine the total force, in kN, produced by pressure acting on 1 m-diameter horizontal hatch of a submarine submerged 600 m below the sea surface. Assume the atmospheric pressure on the sea surface being 100 kPa, the ambient temperature being 300 K, and the density of sea water being 1 g/cm3. (10 points) Solution to problem 4: Analysis: the total pressure on the hatch comes from the atmosphere plus the water:

PaPaPamsmmkgPaghPPPP wateratmwateratmtotal

663

233

1099.51089.510100)600)(/81.9)(/1000(10100

=+=

+=+=+=

kNNmmNPAF 47001070.4)4

)1()(/1099.5( 6226 ====

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5. As shown in the figure on the right, the local atmosphere pressure is 758 mm Hg. The specific gravity (SG) of Fluid A is 0.10194. The specific weight of fluid B is 8 kN/m3. Calculate the absolute pressure, P1, of the manometer in kPa. (10 points) Solution to problem 5: The pressure indicated by a manometer is to be determined. Properties The specific gravity (SG) of Fluid A is 0.10194. The specific weight of fluid B is 8 kN/m3. Analysis The absolute pressure P1 is determined from

kPa 102.7==

++

=

++=

++=

2

233

2atm

atm1

/102

)1000N

1kNm)( )(0.05)(9.81m/s1000kg/m(0.10194m) )(0.15kN/m (8

Hg mm 1kPa 0.1333Hg) mm 758(

mkN

ghSGhPghghPP

AOHBB

AB

g

SG = 0.10194

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6. Pressure transducers are used to measure the pressure by generating the analogue signals, usually in the range of 4 mA to 20 mA, or 0 V-dc to 10 V-dc, in response to the applied pressure. The system is schematically shown in the figure below. A rigid container is filled with the pressurized air; and the pressure is measured by the manometer attached. A valve is used to regulate the pressure in the container. Both the pressure and the electrical signals are measured simultaneously for various settings. The measurement results are tabulated. For the given sets of measurement, the calibration curve is expressed in the form of a liner equation P=aI+b, where a and b are the constants. (6a) Calculate a and b in the equation showing the gage pressure (in kPa) as a function of the electrical current. Provide the equation and a graphical representation of the curve fit; determine the gage pressure that corresponds to the current of 10 mA. (6b) Go to www.omega.com and find two different pressure transducers that could be used for this experiment. Provide the model number, accuracy, and cost for the models selected on the homework solution sheet. Do NOT submit the Omega web page or catalog pages. (6c) When would a transducer be used in place of a manometer? (6d) When would a manometer be used in place of a transducer? (6e) Find two different transducers that are commonly used to measure temperature. Provide the model number, accuracy, and cost for the models selected on the homework solution sheet. Do NOT submit the Omega web page or catalog pages. (6f) Comment on the cost of these transducers relative to the accuracy level. (15 points)

Solution to problem 6: A pressure transducers is used to measure pressure by generating analogue signals, and it is to be calibrated by measuring both the pressure and the electric current simultaneously for various settings, and the results are tabulated. A calibration curve in the form of P = aI + b is to be obtained, and the pressure corresponding to a signal of 10 mA is to be calculated. Assumptions: Mercury is an incompressible liquid. Properties: The specific gravity of mercury is given to be 13.56, and thus its density is 13,560 kg/m3. Analysis For a given differential height, the pressure can be calculated from

hgP = For h = 28.0 mm = 0.0280 m, for example,

kPa75.3 kN/m1

kPa1m/s kg1000

kN1m) )(0.0280m/s (9.81) kg/m(100056.13 2223 =

=P

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Repeating the calculations and tabulating, we have

h(mm) 28.0 181.5 297.8 413.1 765.9 1027 1149 1362 1458 1536

P(kPa) 3.73 24.14 39.61 54.95 101.9 136.6 152.8 181.2 193.9 204.3 I (mA) 4.21 5.78 6.97 8.15 11.76 14.43 15.68 17.86 18.84 19.64

A plot of P versus I is given below. It is clear that the pressure varies linearly with the current, and using EES, the best curve fit is obtained to be P = 13.00I - 51.00 (kPa) for 64.1921.4 I . For I = 10 mA, for example, we would get

P = 79.0 kPa Discussion Note that the calibration relation is valid in the specified range of currents or pressures.

4 6 8 10 12 14 16 18 200

45

90

135

180

225

I, mA

P, k

Pa

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7. Write an essay on different temperature measurement devices. Explain the operational principle of each type of device, its advantages and disadvantages, its costs and its range of applicability. Go to www.omega.com or other venders websites and find the device with the lowest price, which is suitable for use in the following cases: (i) monitoring the surface of car engine at different locations. (ii) checking the temperature of the flame in a combustor. (iii) measuring the temperature inside an industrial furnace with the maximum operating temperature of 1500 oC. List the costs, the accuracy and the temperature range of the devices that you have chosen for each case. (15 points) 8. Explain why international standards are important. How were these standards developed? What importance do units play in solving a problem involving international team or designing a product to be globally sold? (5 points)