Question

To fill a child's inflatable wading pool, you use a garden hose with a diameter of 3.0 cm . Water flows from this hose with a speed of 1.3 m/s .

How long will it take to fill the pool to a depth of 28 cm if the pool is circular and has a diameter of 1.5 m ?

Answer 1

Solution) Diameter, d = 3 cm = 3×10^(-2) m

Radius , r= (3×10^(-2))/(2) = 1.5×10^(-2) m

v = 1.3 m/s

H = 28 cm = 0.28 m

Diameter , D = 1.5 m

Radius , R = (D/2) = (1.5/2) = 0.75 m

Time , t = ?

Volume , V = (pi)(R^2)(H)

V = (pi)(0.75^2)(0.28)

V = 0.494 m^3

Volume flow rate = Av

A = (pi)(r^2)

Volume flow rate = (pi)(r^2)(v)

Volume flow rate = (pi)((1.5×10^(-2))^2)(1.3)

Volume flow rate = 9.189×10^(-4)

Time = (Volume)/(Volume flow rate)

t = (0.494)/(9.189×10^(-4))

t = 537.6 s