Answer
The diameter of the hose is 2.0 cm
Work Step by Step
We find the volume flow rate of the water;
$flow~rate = \frac{V}{t}$
$flow~rate = \frac{600~L}{(8.0~min)(60~s/min)}$
$flow~rate = 1.25~L/s$
We convert the flow rate to units of $m^3/s$;
$flow~rate = (1.25~L/s)(\frac{1~m^3}{1000~L})$
$flow~rate = 1.25\times 10^{-3}~m^3/s$
The flow rate is equal to the cross-sectional area of the hose times the speed of the water. We can find the radius of the hose.
$flow~rate = v~A = 1.25\times 10^{-3}~m^3/s$
$v~\pi~r^2 = 1.25\times 10^{-3}~m^3/s$
$r^2 = \frac{1.25\times 10^{-3}~m^3/s}{v~\pi}$
$r = \sqrt{\frac{1.25\times 10^{-3}~m^3/s}{v~\pi}}$
$r = \sqrt{\frac{1.25\times 10^{-3}~m^3/s}{(4.0~m/s)~(\pi)}}$
$r = 0.009974~m = 0.9974~cm$
We then find the diameter of the hose:
$d = 2r = (2)(0.9974~cm) = 2.0~cm$
The diameter of the hose is 2.0 cm.
