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A. Energy Balance: A basement is unfortunately flooded with liquid (water) of density $\rho$. You need to pump the liquid out of the basement thru a window that is at h = 1 m high at a volumetric flow, Q = $1.2 \times 10^4$ cm$^3$/s using a pimp of power P. Assume that, frictional loss due to viscous effects, F = U$^2$/2, where U is the output velocity. The acceleration due to gravity g = 10 m/s$^2$ and density of water is 1 g/cm$^3$. (a) Label the input and output points to calculate the power of the pump, P in terms of U, Q, h, $\rho$, and g. (b) Using the numerical values given, calculate the output velocity, U for a 180 W pump (which is about 1/4 HP). Assume the efficiency of the pump to be 100%. Pay attention to the sign. (c) BONUS: Calculate the diameter of the tube, D.

          A. Energy Balance: A basement is unfortunately flooded with liquid (water) of density $\rho$. You need to pump the liquid out of the basement thru a window that is at h = 1 m high at a volumetric flow, Q = $1.2 \times 10^4$ cm$^3$/s using a pimp of power P. Assume that, frictional loss due to viscous effects, F = U$^2$/2, where U is the output velocity. The acceleration due to gravity g = 10 m/s$^2$ and density of water is 1 g/cm$^3$.
(a) Label the input and output points to calculate the power of the pump, P in terms of U, Q, h, $\rho$, and g.
(b) Using the numerical values given, calculate the output velocity, U for a 180 W pump (which is about 1/4 HP). Assume the efficiency of the pump to be 100%. Pay attention to the sign.
(c) BONUS: Calculate the diameter of the tube, D.

A. Energy Balance: A basement is unfortunately flooded with liquid (water) of density ρ. You need to pump the liquid out of the basement thru a window that is at h = 1 m high at a volumetric flow, Q = 1.2 × 10^4 cm^3/s using a pimp of power P. Assume that, frictional loss due to viscous effects, F = U^2/2, where U is the output velocity. The acceleration due to gravity g = 10 m/s^2 and density of water is 1 g/cm^3.
(a) Label the input and output points to calculate the power of the pump, P in terms of U, Q, h, ρ, and g.
(b) Using the numerical values given, calculate the output velocity, U for a 180 W pump (which is about 1/4 HP). Assume the efficiency of the pump to be 100%. Pay attention to the sign.
(c) BONUS: Calculate the diameter of the tube, D.

Added by Hayden N.

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