How Does Jet Propulsion Determine a Boat's Steady Forward Speed?

In summary, the boat's steady forward speed v can be calculated using the formula v = Q/(k*v'). The boat is jet-propelled by a pump that generates a volume flow rate Q and expels water through the stern at velocity v'. The boat's drag force is determined by the constant k and the square of the boat's speed, F=kv^2.
  • #1
TheTank
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A boat is jet-propelled by a pump that develops a volume flow rate Q and ejects water out the stern at velocity v'. If the boat drag force is F=kv^2 where k is a constant, develop a formula for the steady forward speed v of the boat.
 
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  • #2
TheTank said:
A boat is jet-propelled by a pump that develops a volume flow rate Q and ejects water out the stern at velocity v'. If the boat drag force is F=kv^2 where k is a constant, develop a formula for the steady forward speed v of the boat.

please use the template
 

Related to How Does Jet Propulsion Determine a Boat's Steady Forward Speed?

1. What is Reynold's transport theorem?

Reynold's transport theorem is a mathematical tool used to describe the changes in a physical quantity within a control volume as it moves through space and time.

2. Why is Reynold's transport theorem important?

Reynold's transport theorem is important because it allows us to analyze the changes in a physical quantity within a control volume, which is essential in many fields of science and engineering, such as fluid mechanics and thermodynamics.

3. How is Reynold's transport theorem different from the continuity equation?

The continuity equation is a specific application of Reynold's transport theorem, which is more general and can be applied to various physical quantities, not just mass. The continuity equation only deals with the conservation of mass, while Reynold's transport theorem can be used to analyze the conservation of other quantities, such as momentum and energy.

4. Can Reynold's transport theorem be applied to both steady and unsteady systems?

Yes, Reynold's transport theorem can be applied to both steady and unsteady systems. In steady systems, the changes in physical quantities with respect to time are assumed to be zero, while in unsteady systems, these changes must be taken into account.

5. What are some practical applications of Reynold's transport theorem?

Reynold's transport theorem has various practical applications, such as analyzing fluid flow through pipes, calculating heat transfer in a system, and studying the movement of pollutants in the environment.

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