A fire hose has an inside diameter of 45 cm. Suppose such a hose carries a water

Question

A fire hose has an inside diameter of 45 cm. Suppose such a hose carries a water flow of 43 Us starting at a gauge pressure of 138 times 10^6 N/m^2 . The hose discharges through a nozzle having an inside diameter of 3.4 cm. Take the viscosity of water to be 1.005 times 10^3 (N/m^2)-s. Calculate the Reynolds number, for flow in the fire hose to show that the flow must be turbulent, with 3000. Calculate the Reynolds number, N_R, for flow in the fire hose and nozzle to show that the flow must be turbulent, with N_R

Explanation / Answer

a) volume flow rate = A v = ( pi d^2 / 4) v

43 x 10^-3 m^3/s = ( pi * (0.045)^2 / 4) v

v = 27.04 m/s

and Nr = rho * v* d / mu

= (1000 kg . m^3) (27.04 m/s) ( 0.045 m) / (1.005 x 10^-3)

= 1210598

b) for nozzle,

43 x 10^-3 = pi * 0.034^2 /4 * v

v = 47.36 m/s

Nr = (1000 ) (47.36) ( 0.034) / (1.005 x 10^-3)
= 1602262

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