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 :

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

[tex]\dfrac{dM}{dt} = \rho AV[/tex]

[tex]\dfrac{dM}{dt} = \pi r^2 \rho V[/tex]

[tex]\dfrac{dM}{dt} = \pi \times 0.075^2\times 1000 \times 3.1[/tex]

[tex]\dfrac{dM}{dt} =54.78\ Kg/s[/tex]

[tex]\dfrac{dM}{dt} =54.78\times 3600\ Kg/h[/tex]

[tex]\dfrac{dM}{dt} =1.97\times 10^5\ Kg/h[/tex]

b) Using continuity equation

              [tex]A_1V_1 = A_2V_2[/tex]

              [tex]\pi \times 0.075^2\times 3.1 = 3 \times \pi \times 0.025^2\ V_2[/tex]

                          vā‚‚ = 9.3 m/s

speed of water through each hose.

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