Question

The pressure of water flowing through a 5.9×10^-2 m-radius pipe at a speed of 1.2 m/s...

The pressure of water flowing through a 5.9×10^-2 m-radius pipe at a speed of 1.2 m/s is 2.2×10^5 N/m^2.

a) What is the flow rate of the water?

b) What is the pressure in the water after it goes up a 5.8 m-high hill and flows in a 4.2×10^-2 m-radius pipe?

Density of water = = 1000 kg/m3

Gravitational acceleration = g = 9.81 m/s2

Pressure at point 1 = P1 = 2.2 x 105 N/m2 = 220000 N/m2

Radius of the pipe at point 1 = R1 = 5.9 x 10-2 m

Speed of flow at point 1 = V1 = 1.2 m/s

Area of the pipe at point 1 = A1 = R12

Pressure at point 2 = P2

Radius of the pipe at point 2 = R2 = 4.2 x 10-2 m2

Speed of flow at point 2 = V2

Height of point 2 compared to point 1 = h = 5.8 m

Area of the pipe at point 2 = A2 = R22

Flow rate of water = Q

Q = A1V1

Q = R12V1

Q = (5.9x10-2)2(1.2)

Q = 1.312 x 10-2 m3/s

By continuity equation,

A1V1 = A2V2

R12V1 = R22V2

R12V1 = R22V2

(5.9x10-2)2(1.2) = (4.2x10-2)V2

V2 = 2.368 m/s

By bernoulli's equation,

P2 = 161018.29 N/m2

a) Flow rate of water = 1.312 x 10-2 m3/s

b) Pressure in the water after it goes up a 5.8 m high hill and flows in a 4.2x10-2m radius pipe = 161018.29 N/m2