# solution

Macroscale Momentum and Energy Balances
Assignment Due : 4:00 pm on Monday, May 16th, 2011
1. Water is flowing in a (complete) U-bend at a volume flow rate of 4 ft3/s. The diameter
of the pipe is constant. The Inlet pressure is 24 psia, the outlet pressure is 20 psia (note
that psia means “psi absolute”). Determine the horizontal force exerted by the water on
the U-Bend. The bend is horizontal, so body forces may be neglected. Assume that the
flow is at steady state, and that ÃŸ=1.05.
2. A horizontal 45 degree reducing bend, illustrated in the diagram below, is 500 mm in
diameter at the upstream end and 250 mm in diameter at the downstream end. Water
flows through the bend at a steady state volume flow rate Q=0.1 m3/s. The absolute
pressure at the upstream end of the bend is 250 kPa, the absolute pressure at the
downstream end is 210 kPa. What is the direction and magnitude of the force exerted
by the water on the reducing bend? Assume a momentum correction factor ÃŸ=1.05,
and ?=1000 kg/m3.
3. A plate is being cleaned by a jet emitted by a nozzle, as shown in the diagram below.
The jet provides a flow Q=4.0 l/s, and the diameter of the jet is 1 cm. Assume ?=1000
kg/m3.
(a) Determine the direction and magnitude of the force required to hold the plate
in place, if friction causes the magnitude of the velocity of the deflected jet to
be reduced to 95% of the incoming jet velocity. The angle ?=35Â°.
(b) Recalculate the magnitude and the direction of the force required to hold the
plate in place if ?=90Â°. What effect would friction have on the calculated force
(Hint – assume that the jet is dispersed equally in all directions, and remains
parallel to the plate after striking the plate).
x
y
4. A 25 mm diameter jet has an average velocity of 33.5 m/s. It strikes a blade that is
moving in the same direction as the jet at a velocity of 21.3 m/s, as shown in the
diagram below. The deflection angle of the blade is 330Â°. The system is at steady state
(ie the blade velocity is constant). Assuming no friction and neglecting body forces,
calculate the X and Y components of the force exerted by the water on the blade.
5. The conditions at the entrance (1) and exit (2) of a system are as shown in the figure
below. The pump in the system could be either (1) operating as normal, supplying
energy to the system, or (2) behaving as a turbine, spinning in response to the flow and
taking work out of the system. Given the data in the diagram, which of these scenarios
is actually occurring? Assume that friction losses in the section of the system under
consideration are negligible, and that the velocity profile can be regarded as flat.
6. Water enters the nozzle illustrated in the diagram below at 500 kPa (gauge), and exits
at atmospheric pressure. If the exit velocity of the jet is 50 m/s, calculate the friction
loss factor (k) for the nozzle.
V1= 3.0 m/s
P1G= 160 kPa
Z1= 10.0 m
V2= 7.5 m/s
P2G= 120 kPa
Z2= 14.0 m
Pump
7. The section of pipework illustrated in the figure below has been fabricated for
installation in a process. When installed, the section will be aligned in the vertical
plane. The liquid passing through the pipework has a specific gravity of 0.95. The
volume flow rate entering the pipework at section 1 is 75 litres per second, and the
absolute pressure at section 1 is 320 kPa.
Calculate the absolute pressure (in Pa) at section 2. For the purposes of this
calculation, it may be assumed that the straight pipe losses in the pipe are negligible.
Fitting losses, however, must be taken into account.
8. A simple separation process was devised which uses the tank shown in the figure
below. An outlet is set up halfway up the side of the tank, To avoid drawing sediment
out of the tank. The outlet connects to a pipe of length L, which empties out into the
atmosphere above a mixing tank. Derive an equation giving the velocity at which
water flows out of the outlet pipe in terms of the height H of sauce left in the tank.
Assume that all losses associated with the entrance to the pipe and the pipe itself are
negligible.
H0
H
L

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