Physics Homework Help?

Question

Water at a gauge pressure of P = 5.2 atm at street level flows into an office building at a speed of 0.88 m/s through a pipe 4.8 cm in diameter. The pipe tapers down to 2.6 cm in diameter by the top floor, 16 m above (Figure 1) . Assume no branch pipes and ignore viscosity.

Part A

Calculate the flow velocity in the pipe on the top floor.

 

Part B

Calculate the gauge pressure in the pipe on the top floor.

 

Answer 1

(a)

Pressure of water at the bottom of the buliding is .

Flow velocity in pipe at the bottom of the buliding is .

Diameter of pipe at the bottom of the buliding is .

Diameter of pipe at the top of the buliding is .

Find flow velocity in pipe at the top of the buliding .

Equation of continuity: .

Flow velocity in pipe at the top of the buliding is .

Answer 2

(b)

Gauge pressure in pipe on the bottom of the floor is .

Flow velocity of water in pipe at the bottom of the building is .

Flow velocity in pipe at the top of the building .

Height of the building is .

Find the gauge pressure in pipe on the top of the floor is .

Bernoulli's principle: .

Where is the density of water.

is the acceleration due to gravity.

is the height of the pipe at the street.

is the height of the pipe at the top of the floor.

is the flow velocity in pipe at the bottom of the building.

is the flow velocity in pipe at the top of the building.

is the pressure of water at the bottom of the building

is the pressure of water at the top of the building

Here .

Gauge pressure of water at the top of the building is 3.61 atm.