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.