Jetski propulsion analysis (fluid dynamics)

[GDSF1]

Homework Statement

[/B]
http://imgur.com/TQf2TNP
http://imgur.com/TQf2TNP
Diagram for the porblem
For this problem, you may assume the following:
• The mass flow rate of water through the jet pump is always the same.
• The combined mass of the rider and jetski is 450kg
• The time dependent change of fluid velocity in the jet pump apparatus is negligible.
• The drag area coefficient: CDA =
2D
ρV 2 is a constant for the whole problem.
• The jet velocity is 21m/s relative to the jetski.
1• The inlet is circular with radius 0.15m and is horizonatally oriented.
• For forward operation, the water exits the jetski in the horizontal direction only.
• The jet exits from a circular hole with radius 0.075m
Answer the following & clearly state all assumptions. Draw and label control
volumes.
1. Determine the mass flow rate of water through the jet-pump system. Clearly draw and label
your CV. You may assume the jet has a uniform velocity at the entrance and exit for this
question and subsequent questions.
2. At the top jetski velocity (Vmax = 18m/s), the thrust force equals the drag force. Determine
the drag force acting on the jetski at 18m/s? Draw and clearly label your control volume.
3. The drag-area coefficient (CDA) of the jetski can be computed as CDA =2DρV 2 . Determine
the drag-area coefficient for the 18m/s operating condition.
4. Assuming the drag-area is the same at all speeds, approximate the time it takes for the jetski
to accelerate from 0m/s to 16m/s, assuming that the exit jet velocity is always 21m/s relative
to the jetski. Plot the thrust vs. time, the acceleration vs. time, the velocity vs. time and
the distance vs. time. You will find it easier to use Excel or Matlab to solve this problem
(again: u =dxdt 'u(t+∆t)−u(t)∆t).

Homework Equations

Stated Above

The Attempt at a Solution

For the first part, i was able to figure out that Mass flow rate in is equal to flow rate out and enough variables to solve it.
The problem with the second question is how to set up the conservation of momentum equation and factor in thrust and drag in it with relative velocities.

Thank

 

[Chestermiller]

For part 2, the jet ski is traveling at constant velocity. So you can use a stationary frame of reference, or you can use a frame of reference which is moving with the jet ski. Both frames of reference are inertial, so either is acceptable. Using the jet ski as a control volume, what is the rate of change of momentum of the water passing through the jet pump?

Chet