Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.014 m. Water enters the hydrant through an underground pipe of radius 0.089 m. In this pipe the water has a speed of 3.3 m/s. (a) How many kilograms of water are poured onto a fire in one hour by all three hoses

Explanation:

The total fluid mass can be obtained by multiplying the mass flow rate by the time flow rate.

Mass flow rate is given as

m = ρAv

Where

m is mass flow rate

ρ is density

A is area and it is given as πr²

v is velocity

Then,

M = mt

Where M is mass and t is time

Them,

M = ρAv × t

M = ρ× πr² × v × t

Given that, .

Radius of pipe is

r = 0.089m

velocity of pipe is

v = 3.3m/s

Time taken is

t = 1 hour = 3600 seconds

Density of water is

ρ = 1000kg/m³

M = ρ× πr² × v × t

M = 1000 × π × 0.089² × 3.3 × 3600

M = 295,628.52 kg

M = 2.96 × 10^5 kg