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

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