Download Problem Set #1 - Purdue College of Engineering

AAE333 Fall 2010
Homework 4
Due: Monday Sept 20
10% bonus if turned in on Friday 9/17/10
1. Consider a tank of water 1m deep. At the bottom of the tank is a square door, 2
cm on each side, which is hinged along the top edge so the bottom is free to rotate
outward from the tank. The tank is open at the top to 1 atm air.
The door
connects the tank to a pressurized line full of air. Determine the line pressure
required to keep the door closed for two situations:
a. The door hangs vertically
b. The door hangs at a 45deg angle to the horizontal (and vertical)
2. Consider a pan which is 2cm deep, 10cm long and 5 cm wide. The pan is half
filled with water, 1cm deep. This pan is placed on a cart which is subjected to
a uniform acceleration “a” along the long axis of the pan (10cm). Determine
how big “a” would have to be (in “g’s” ) to make the water slosh out the rear
end of the pan.
3. Salt water exits a 1cm by 1cm square hole at a speed of 2cm/s. The salt
content is 0.2% by weight. What is the mass flow rate of salt coming out the
hole (ie. gm/sec) ?
4. Given a velocity field u  2 xe x  3 ye y  Kze z , where K is some constant and
velocities are measured in m/s. Find the rate of expansion of a fluid particle
(i.e. the fractional increase in volume per second). What value would K have
to have for the fluid to be incompressible?
5. For the same velocity field given in Pb 4, determine the total volume per
second of fluid leaving a cube with each edge .2 m long, with its six faces at
x=0, x=.2, y=0, y=.2, z=0 and z=.2 respectively. What is the this volume
flow rate if the fluid is incompressible?
AAE333 Fall 2010