Which of the following situations would make most sense to approach using integral forms of conservation? Group of answer choicesTo determine the mean flow-rate in a converging pipe flowAll of the available optionsTo determine the average velocity at the outflow of a pipeTo determine the force acting on a wing during flightNone of the available options
Question
Which of the following situations would make most sense to approach using integral forms of conservation? Group of answer choicesTo determine the mean flow-rate in a converging pipe flowAll of the available optionsTo determine the average velocity at the outflow of a pipeTo determine the force acting on a wing during flightNone of the available options
Solution
The integral forms of conservation laws, such as the conservation of mass, momentum, and energy, are most useful when dealing with a control volume - a certain region of space through which fluid flows. They allow us to consider the net effect of the fluid flow through the control volume.
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To determine the mean flow-rate in a converging pipe flow: The integral form of the conservation of mass (also known as the continuity equation) can be used to determine the mean flow rate in a pipe. This is because the flow rate is equal to the integral of the velocity over the cross-sectional area of the pipe.
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To determine the average velocity at the outflow of a pipe: Again, the integral form of the conservation of mass can be used. By knowing the flow rate and the cross-sectional area at the outflow, the average velocity can be determined.
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To determine the force acting on a wing during flight: The integral form of the conservation of momentum can be used to determine the force on a wing. This is because the force is equal to the rate of change of momentum, and the momentum of the fluid changes as it flows over the wing.
Therefore, all of the available options would make sense to approach using integral forms of conservation.
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