Kevin S. Huang

2012: Problem 19

Topic: Fluids
Concepts: Newton’s laws, Power

Solution:

The motor has to supply a force $F$ on the water in the pipe that balances its weight $W$ since the water is moving at constant speed. Because the pipe is a cylinder, the mass of the water is

M=\rho V=\rho (\pi r^2h)

Then

F=W=Mg=\pi \rho r^2hg

The power required to pump the water at velocity $v$ is given by

P=Fv=\pi\rho r^2hgv

so the radius of the pipe is

r=\sqrt{\frac{P}{\pi\rho hgv}}=\sqrt{\frac{1500\,\mathrm{W}}{\pi(1000\,\mathrm{kg/m^3})(2\,\mathrm{m})(10\,\mathrm{m/s^2})(2.5\,\mathrm{m/s})}}=10\,\mathrm{cm}

Thus, the answer is D.

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Kevin S. Huang

2012: Problem 19

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2012: Problem 19

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