Question

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

Answer 1

Dear Student,

Please find the solution to the asked query.

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.