MEEN 371
1.
HW 5
View the MOI lab video. Compute the moment of inertia of the rotating object two different
ways:
 From the constant angular acceleration caused by a falling mass
 From the natural frequency of rotary oscillation (write rotational DE to find keq)
 Video note: The yardstick measures inches; the tape on the cart track measures cm.
 Assumptions:
i. Friction is negligible.
ii. The radii of the pulleys are constant.
iii. The springs are equal.
 Compute the percent difference and comment on any discrepancies
2. Initially the valve is closed, with tank 2 (0.92m3) at 6.2MPa and tank 1
(2.1m3) at 5.7MPa. Both tanks contain hydrogen gas. At t=0, the
valve is opened. The initial flow rate is Qm(0)=0.2kg/s. The tanks are
well-insulated such that heat transfer from the system is negligible;
the average system temperature during the process is 20°C. Plot the
absolute pressure (i.e. not the deviation) in each tank as a function of
time; plot the two pressures on a common graph.
3. Initially the valve between tanks is closed, but the valve above is open,
with tank 2 (0.92m3) at atmospheric pressure (101kPa) and tank 1
(2.1m3) at 90kPa. Both tanks contain air. At t=0, the in-between valve is
opened. The initial flow rate into tank 1 is Qm1(0)=0.2kg/s; assume the
two valves are identical. The process is isothermal at -10°C. Plot the
pressure in each tank as a function of time; plot the two pressures on a
common graph.
4. A 1m x 2m x 12mm steel plate (=8050 kg/m3,CP=511 J/kg°C, k=43 W/m°C) has been in direct
sunlight which caused its initial temperature to be 60°C. The plate is taken into a warehouse
with an ambient temperature of 20°C, and is positioned in such a way that plenty of fresh air can
contact all six sides of the plate (h=4.5W/m2°C). Use the Biot number to justify a single-lump
mass model. Develop this model’s DE. Determine the time constant. What temperature will
the plate be after 3 time constants? How might you have approached this problem if the Biot
number had turned out to be greater than 0.1?
MEEN 371
HW 5
5. Chilled water is being pumped through an insulated steel pipe (see diagram for cross-section),
when the pump fails and the water stops moving. Write an expression for the equivalent
thermal resistance, Req, for heat entering the water from the air (in terms of dimensions,
material properties and convective properties given). Also write an
expression for the water’s thermal capacitance in terms of the given
information. Write a DE with water temperature TW as the dependent
variable. Assumptions:
 Known values: Pipe length L; water density  and specific heat CP;
air temperature TA.
 The water temperature is always uniform throughout, due to
convective mixing.
 The thermal capacitance of the pipe and the insulation are
negligible.
 There is no thermal resistance between the pipe outer surface
and the insulation inner surface
6. This winter you accidentally left your favorite copper ball (1” in diameter) sitting outside in a
Styrofoam cup of water overnight. In the morning, you brought the cup with its contents,
initially a uniform 40°F, inside where the air temperature is 70°F. Based on the following
assumptions, write the DE’s for the temperatures of the water and the copper and use software
to solve them. Plot the temperatures of each until steady state is nearly reached (120min).
 The water temperature remains uniform throughout, due to convective mixing.
 Heat enters the water only through its free surface (hAW=21BTU/hr*ft2*°F, cup’s inner
diameter at water surface = 3in); the Styrofoam is an excellent insulator.
 Water and copper properties: CPW=1BTU/lbm°F, mW=0.4lbm, hWC=157BTU/hr*ft2*°F,
CPC=0.092BTU/lbm°F, C=0.324lbm/in3, k=223BTU/hr*ft*°F
7. Find the transfer function for the block
diagram.