# Chapter 14 - Fluids and Elasticity - Exercises and Problems: 26

It would take 6.8 minutes to fill the pool.

#### Work Step by Step

We can find the volume flow rate of the water in the hose. The volume flow rate is the water speed times the cross-sectional area of the hose as: $flow~rate = v~A$ $flow~rate = v~\pi~r^2$ $flow~rate = (3.0~m/s)(\pi)(0.0125~m)^2$ $flow~rate = 1.47\times 10^{-3}~m^3/s$ We can convert the volume flow rate to units of liters as: $flow~rate = (1.47\times 10^{-3}~m^3/s)(\frac{1000~L}{1~m^3})$ $flow~rate = 1.47~L/s$ We can find the time it takes to fill the pool as: $t = \frac{volume}{flow~rate}$ $t = \frac{600~L}{1.47~L/s}$ $t = 408~s = 6.8~min$ It would take 6.8 minutes to fill the pool.

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