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,

A_{1}V_{1}=A_{2}V_{2}

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.

6. Water is used to circulate heat through a house. The water
starts in the basement with a speed of 0.8 m/s in a pipe and a
pressure of 3.46 atm. The pipe goes up 6 m to the top floor with a
new pressure of 2.78 atm and new diameter of 2.5 cm in diameter.
Find the new water speed in the second part of the pipe and the
initial diameter of the pipe

2 parts! thanks :)
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