Homework Set #2
1. In a two-dimensional low speed flow experiment, the velocity field was measured
and curve fitted as:
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. 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.
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 ρgh. 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.
Inflow velocity = 5
ft/sec
10 ft
3 ft
V=?
j
yx
y
i
yx
x
V
2222
33
+
+
+
=
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