Question

# Water circulates through a hot-water heating system in a house. The water leaves the basement with...

Water circulates through a hot-water heating system in a house. The water leaves the basement with a speed of 0.5 m/s through a 4-cm-diameter pipe, under a total pressure of 3Patm. (Assume that all the pipes have circular cross-sectional areas and that the pipes don't "branch off" at any point.) a) If the pipe on the second floor of the house has a smaller radius than the basement pipe, will the speed of the water in the second-floor pipe be smaller than, larger than, or equal to 0.5 m/s? b) If the diameter of the second floor pipe is 2.5 cm, determine the speed of the water in that pipe (in m/s). c) If the second-floor pipe is located 15 m above the basement pipe, determine the pressure in that pipe. d) If there were a leak in the second-floor pipe (so that the water in the pipe is exposed to the determine the speed of the water as it leaves the pipe

Dear Student,

I hope the given pressure is 4 atm

a) According to the Equation of Continuity,

A1V1=A2V2

So, If the cross section area of the pipe decreases, then the speed of the flow increases.

Therefore, the speed of the flow in the second floor will be greater than 0.5 m/s.

b)   Now, for the given diameters, the speed of the flow in the second floor is,

c)   According to Bernoulli's Equation,

d)   So, Pressure inside and outside the pipe should be same.

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