Solutions to homework 5

MAE 308 HW5
Assigned March 17, 2011
Due: March 24, 2011 before class
P1. Water flows through a circular nozzle, exits into the air as a jet, and strikes a plate. The force
required to hold the plate steady is 70 N. Assuming frictionless one-dimensional flow, estimate
(a) the velocities at sections (1) and (2); (b) the mercury manometer reading h.
Answer: (a) V1=0.9 m/s, V2= 9.96 m/s; (b) h= -0.4 m
Solution: (a) First exam the momentum of the jet striking the plate:

P2. For the container shown in the figure, use Bernoulli’s equation to derive a formula for the
distance X where the free jet leaving horizontally will strike the floor, as a function of h and H.
For what ratio h/H will X be maximum
Answer:
Solution:
X reaches a maximum at h=H/2 with X max =H.

P3. A necked-down section in a pipe flow, called a venturi, develops a low throat pressure with
can aspirate fluid upward from a reservoir as shown. Using the Bernoulli’s equation with no
losses, derive an expression for the velocity V1 with is just sufficient to bring reservoir fluid into
the throat.
Answer:
Solution: Water will begin to aspirate into the throat when P a -P 1 =ρgh. Hence:

P4. A venture meter as shown is a carefully designed construction whose pressure difference is a
measure of the flow rate in a pipe. Using Bernoulli’s equation for steady incompressible flow
with no losses, show that the flow rate Q is related to the manometer reading h by
where
is the density of the manometer fluid.