Question

Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.025 m. Water enters the hydrant through an underground pipe of radius 0.075 m. In this pipe the water has a speed of 3.1 m/s. (a) How many kilograms of water are poured onto a fire in one hour by all three hoses? kg (b) Find the water speed in each hose. m/s

Answer 1

Answer

given,

radius of each hose = 0.025 m

water enters hydrant at radius = 0.075 m

speed of water in the pipe = 3.1 m/s

a) mass of water per hours through the house can be calculated

$\dfrac{dM}{dt} = \rho AV$

$\dfrac{dM}{dt} = \pi r^2 \rho V$

$\dfrac{dM}{dt} = \pi \times 0.075^2\times 1000 \times 3.1$

$\dfrac{dM}{dt} =54.78\ Kg/s$

$\dfrac{dM}{dt} =54.78\times 3600\ Kg/h$

$\dfrac{dM}{dt} =1.97\times 10^5\ Kg/h$

b) Using continuity equation

              $A_1V_1 = A_2V_2$

              $\pi \times 0.075^2\times 3.1 = 3 \times \pi \times 0.025^2\ V_2$

                          v₂ = 9.3 m/s

speed of water through each hose.