Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.017 m. Water enters the hydrant through an underground pipe of radius 0.088 m. In this pipe the water has a speed of 2.7 m/s. (a) How many kilograms of water are poured onto a fire in one hour by all three hoses

2.36 x 10^5 kg

Explanation:

radius of hose, r = 0.017 m

radius of underground pipe, R = 0.088 m

number of hoses, n = 3

velocity of water in underground pipe, V = 2.7 m/s

Let v is the velocity of water in each hose.

According to the equation of continuity

A x V = n x a x v

π R² x V = n x π x r² x v

0.088 x 0.088 x 2.7 = 3 x 0.017 x 0.017 x v

v = 24.12 m/s

(a) Amount of water poured onto a fire in one hour by all the three hoses              

                    = n x a x v x density of water x time

                    = 3 x 3.14 x 0.017 x 0.017 x 24.12 x 1000 x 3600

                    = 2.36 x 10^5 kg

Thus, the amount of water poured onto the fire in one hour is 2.36 x 10^5 kg.

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