Jetski propulsion analysis (fluid dynamics)

In summary: He has been able to solve the first part of the problem, which involves finding the mass flow rate of water through the system. However, he is struggling with the second question, which asks for the drag force acting on the jet ski at a certain velocity. He is unsure of how to set up the conservation of momentum equation and factor in the thrust and drag forces with relative velocities.
  • #1
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Homework Statement


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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
 
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  • #2
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
 

1. How does the shape of a jet ski affect its propulsion?

The shape of a jet ski greatly affects its propulsion through fluid dynamics. A streamlined and hydrodynamic shape reduces drag and allows for more efficient movement through the water. The shape also plays a role in how the water is directed towards the jet nozzle, which is responsible for propelling the jet ski forward.

2. What is the role of the impeller in jet ski propulsion?

The impeller is a key component in jet ski propulsion. It is a rotating blade that creates suction and draws water into the jet ski. As the water is forced through the impeller, it is accelerated and directed towards the nozzle, creating thrust and propelling the jet ski forward.

3. How does the angle of the jet nozzle affect the performance of a jet ski?

The angle of the jet nozzle is important in determining the direction and intensity of the water jet. A higher angle can provide more thrust, but also increases drag. A lower angle reduces drag, but may also decrease the efficiency of the jet ski's propulsion. Finding the optimal angle is crucial for maximizing performance.

4. What factors affect the efficiency of a jet ski's propulsion system?

Several factors can affect the efficiency of a jet ski's propulsion system, including the shape of the jet ski, the design of the impeller and nozzle, the angle of the nozzle, and the power of the engine. Other factors such as water conditions and the weight of the jet ski and rider can also impact the efficiency of the propulsion system.

5. How does the size and shape of the intake grate impact a jet ski's propulsion?

The intake grate is responsible for directing the water towards the impeller. Its size and shape can greatly impact the amount of water that is drawn into the jet ski. A larger and more open grate can allow for more water to enter, providing more thrust, but also increasing the risk of debris getting sucked in. A smaller and more closed grate may reduce the risk of debris, but can also limit the amount of water entering and potentially decrease the propulsion power.

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