Download AE 2020 Homework Set #1

AE 2020 Homework Set #2
Due on Thursday February 4, 2008
1.
In a two-dimensional low speed flow experiment, the velocity field was measured
and curve fitted as:

V
3x 
3y 
i

j
x2  y2
x2  y2
Verify if this velocity field satisfies the continuity equation.
Hint: Identify the u- and v- components. Determine whether u/x + v/y adds up to
zero.
2.
10 ft
Consider the cross section of a sluice gate, which is a device for controlling the
flow of water in channels. Determine the force on the gate per unit width of the
gate.
Inflow velocity = 5
ft/sec
V=?
3 ft
Hint: think of each line as a surface, with the length given above, and 1 foot of depth in
the direction normal to the plane of the paper. The hydrostatic gauge pressure field p
equals gh. That is, the gauge pressure at any point in the flow will linearly vary with the
depth of the water, h. Use the average values of the pressure (at half-depth) for the
pressure forces.
Ans: V =16.667 ft/sec, Force in the x- direction on the gate = 1708 lb per foot of width in
the direction normal to the plane of the paper.
3.
Consider the flow of water through the nozzle-elbow assembly shown below. The
water issues out as a free jet from the nozzle at atmospheric pressure. What is the
force along the x- direction on the nozzle assembly?
Jet Exit diameter=
0.15 m
Inflow Velocity= 1.5 m./sec
Diameter of pipe at inflow = 0.3 m
Gauge Pressure = 100,000 Pascal
Ans: 7864 N
4.
A pipe tapers from a diameter of 0.5 m at the inlet to a diameter of 0.25 m at the
outlet, and turns by an angle of 45 degrees. The gauge pressure at the inlet and the
outlet are 40000 N/m2 and 23000 N/m2, respectively. The pipe carries oil, with a
density of 850 kg/ m3, at a rate of 0.45 m3/sec. Compute the magnitude and
direction of the force acting on the turn.
45 deg
Ans: 6362 N at a direction 31 degrees relative to the inflow.