A5/8-in. (inside) diameter garden hose is used to fill a round swimming pool 4.6 m in diameter. part a how long will it take to fill the pool to a depth of 1.6 m if water issues from the hose at a speed of 0.59 m/s ?

t = 2.26 10⁵ s

Explanation:

Let's calculate the flow of water that comes out of the hose

         Q = A v

The area of a circle is

        A = π r²

       Q = π r² v

Let's reduce the units to the SI system

       d = 5/8 in (2.54 10⁻² m / in) = 1.5875 10⁻² m

       r = d / 2 = 0.79375 10⁻² m

       Q = π (0.79375 10⁻²)² 0.59

       Q = 1.1678 10⁻⁴ m³ / s

Let's calculate the volume of the pool

       V = π R² h

       V = π (4.6 / 2)²  1.6

       V = 26.59 m³

Let's use a rule of proportions (rule of three), to find the time

       t = 26.59 (1 / 1.1678 10⁻⁴)

       t = 22.77 10⁴ s

       t = 2.26 10⁵ s

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