HW2 SOLUTION- ME 104 SPRING 14

1.

a. Weight and Specific Volume

b. Pressure and mass

Insufficient--while they are independent, mass is not an intensive property.

c. Density and specific volume

d. Specific volume & temperature

e. Temperature and Pressure

Sufficient--independent & both are intensive properties.

2. Convert the temperature of 451 Fahrenheit to the units requested:

SOLUTION Given Temp of 451 F

a. Rankine

911 R

b. Kelvin

506 K

c. & d. Centigrade & Celsius are the same scale, therefore answers to c & d are the same:

233 C

According to the State Postulate, indicate whether the properties given ARE or ARE NOT sufficient to

determine the STATE of a system. If they are NOT sufficient explain why.

Insufficient - Not only is weight an extensive property, but weight & specific volume are not

independent properties

Insufficient - although both are intensive, they are dependent properties--i.e., one is simply the

inverse of the other!!

Sufficient - Both independent AND intensive.

SOLUTION: State Postulate says: The state of a simple compressible system is completely specified by

TWO, INDEPENDENT, INTENSIVE properties

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� � =5

9451 − 32 � � + 273.15 =

� � = � � + 273.15 = �ℎ��� � =5

9� � − 32

� � =5

9� � − 32 =

5

9451 − 32 =

pg. 1 of 3

HW2 SOLUTION- ME 104 SPRING 14

3.

SOLUTION

From: http://www.burjkhalifa.ae/en/

Building Height in meters 828 m

Depth in Feet 2716.502 ft

Density of water at 25 C 997 kg/m3

(from Table A-3)

62.2128 lbm/ft3

SI CALCS US Calcs

P0 101.35 kPa P0 14.7 psia

101350 N/m2 (Pa)

Units analysis for ρg∆h term Units analysis for ρg∆h term

Pressure at Bottom is then Pressure at Bottom is then

P = 8199662.0 Pa

PCD = 8199.7 kPa PCD = 1188.3 psia

Converting kPa to psia…

1 kPa is equivalent to 0.14504 psia (direct conversion from property tables)

Then from kPa answer above, divide by above conversion to get

PCD = 1189.3 psia

Can also do conversion "long hand":

6.894386 kPa/psia

Dividing by above kPa/psia conversion yields P = 1189.3 kPa (absolute pressure)

Calculate the absolute water pressure at the bottom of a pipe that has a vertical height equivalent to the

height of the Burj Khalifa. Assume the top of the pipe is open to the atmosphere. Use standard

atmospheric pressure at sea level and the value for water density at 25 C from Table A-3. Do the

calculations separately in SI & US customary units starting from height measurements in meters & feet

respectively. Confirm your calculations agree by converting your SI answer in kPa to psia.

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pg. 2 of 3

HW2 SOLUTION- ME 104 SPRING 14

4.

a. Calculate the GAUGE pressure of the hydraulic fluid inside each cylinder.

Weight 2500 lbf

Cyl. Diam 3 in

Cyl. Ap = 7.07 in2

SOLUTION:

Assuming weight of car is evenly distributed between

the two cylinders, each cylinder supports 1250 lbf

From FBD at right, Sum of vertical forces is

Solving for Pcyl

176.8 psig

Note that if I added the pressure force resulting from atmospheric air acting on the top of

the piston, then The Pcyl found would be absolute pressure in units of psia.

b. The volume of a cylinder with height h is given by

If the height of the cylinder is changing at a RATE , then the RATE at which the volume

is changing is given by

In this case, the rate at which the car is being raised is

Therefore 339.292 in3/min per piston

0.19635 ft3/min

Converting, for TWO pistons… 2.94 gpm

b. Calculate the TOTAL volumetric flow rate of hydraulic fluid required (entering the cylinder) to raise the

car at a constant velocity of 48 inches per minute (units of GPM).

A car is supported on a hydraulic lift by two identical piston-cylinder devices (i.e., hydraulic cylinders). Each

cylinder has a piston that is 3 inches in diameter. The car weighs 2500 pounds and the weight is evenly

distributed between the two cylinders.

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pg. 3 of 3