Application Exercise 4
1. Does it take more, the same, or less power for a helicopter to hover at the top of a high mountain than it
does at sea level? Explain.
The density of the air is the contributing factor for the lift for a helicopter. At higher levels of elevation,
the atmospheric pressure is lower than at sea level. Because of this the helicopter must generate more
upward lift fore by creating more rotations in the blades. The helicopter will require more power the
higher in elevation it goes and less power the closer to sea level it is.
2. A horizontal water jet of constant velocity V impinges normally on a vertical flat plate and splashes off
the sides in the vertical plane. The plate is moving toward the oncoming water jet with velocity of 0.45
V. If a force F is required to maintain the plate stationary, how much force is required to move the plate
toward the water jet?
Velocity: constant
Jet velocity (Vp): 0.45
Steady state: momentum in = momentum out
(sigma)Fx = (momentum out * Vout) – (momentum in *Vin)
In a moving state: velocity relative (V in) = V-(-0.45v) = 1.45
M in = M out = Pa
V out = 0 // V in = V
Fx = 0 – Pa; V(V) = -Pa;V^2 = force as given
Fx = (V)*(V) = (1.45) * (1.45) = 2.1025 is the force
3. Water accelerated by a nozzle to 33 m/s strikes the vertical back surface of a cart moving horizontally at
a constant velocity of 9 m/s in the flow direction. The mass flow rate of water through the stationary
nozzle is 30 kg/s. After the strike, the water stream splatters off in all directions in the plane of the back
surface.
a. Determine the force that needs to be applied by the brakes of the cart to prevent it from accelerating.
Vn = 33m/s
Vc = 9 m/s
Momentum = 30 kg/s
Force = M(Vn-Vc) = 30(33-9) = 30*24 = 720 Newtons
b. If this force were used to generate power instead of wasting it on the brakes, determine the maximum
amount of power that could ideally be generated.
Power = force x velocity c = 720 * 9 = 6480 watts
4. A 95-ft3/s water jet is moving in the positive x-direction at 17 ft/s. The stream hits a stationary splitter,
such that half of the flow is diverted upward at 45° and the other half is directed downward, and both
streams have a final average speed of 17 ft/s. Disregarding gravitational effects, determine the x- and z-
components of the force required to hold the splitter in place against the water force.
The given assumptions here are steady flow, water exposed to atmosphere (p=0), gravitational effect is
disregarded
M = p*v = (62.4 ibm/ft^3 s) * (95ft^3/s) = m = 5928 ibm
Fx = m*v*(cos theta – 1) = (5928 ibm) * (17ft/s) * (cos45 – 1) * (1 ibm / 32.2 ibm/s^2) = -916.66 ibf
1. Does it take more, the same, or less power for a helicopter to hover at the top of a high mountain than it
does at sea level? Explain.
The density of the air is the contributing factor for the lift for a helicopter. At higher levels of elevation,
the atmospheric pressure is lower than at sea level. Because of this the helicopter must generate more
upward lift fore by creating more rotations in the blades. The helicopter will require more power the
higher in elevation it goes and less power the closer to sea level it is.
2. A horizontal water jet of constant velocity V impinges normally on a vertical flat plate and splashes off
the sides in the vertical plane. The plate is moving toward the oncoming water jet with velocity of 0.45
V. If a force F is required to maintain the plate stationary, how much force is required to move the plate
toward the water jet?
Velocity: constant
Jet velocity (Vp): 0.45
Steady state: momentum in = momentum out
(sigma)Fx = (momentum out * Vout) – (momentum in *Vin)
In a moving state: velocity relative (V in) = V-(-0.45v) = 1.45
M in = M out = Pa
V out = 0 // V in = V
Fx = 0 – Pa; V(V) = -Pa;V^2 = force as given
Fx = (V)*(V) = (1.45) * (1.45) = 2.1025 is the force
3. Water accelerated by a nozzle to 33 m/s strikes the vertical back surface of a cart moving horizontally at
a constant velocity of 9 m/s in the flow direction. The mass flow rate of water through the stationary
nozzle is 30 kg/s. After the strike, the water stream splatters off in all directions in the plane of the back
surface.
a. Determine the force that needs to be applied by the brakes of the cart to prevent it from accelerating.
Vn = 33m/s
Vc = 9 m/s
Momentum = 30 kg/s
Force = M(Vn-Vc) = 30(33-9) = 30*24 = 720 Newtons
b. If this force were used to generate power instead of wasting it on the brakes, determine the maximum
amount of power that could ideally be generated.
Power = force x velocity c = 720 * 9 = 6480 watts
4. A 95-ft3/s water jet is moving in the positive x-direction at 17 ft/s. The stream hits a stationary splitter,
such that half of the flow is diverted upward at 45° and the other half is directed downward, and both
streams have a final average speed of 17 ft/s. Disregarding gravitational effects, determine the x- and z-
components of the force required to hold the splitter in place against the water force.
The given assumptions here are steady flow, water exposed to atmosphere (p=0), gravitational effect is
disregarded
M = p*v = (62.4 ibm/ft^3 s) * (95ft^3/s) = m = 5928 ibm
Fx = m*v*(cos theta – 1) = (5928 ibm) * (17ft/s) * (cos45 – 1) * (1 ibm / 32.2 ibm/s^2) = -916.66 ibf
