Question

A liquid of density 1.11 × 103 kg/m3 flows steadily through a pipe of varying diameter and height. At location 1 along the pipe the flow speed is 9.09 m/s and the pipe diameter is 10.9 cm. At location 2 the pipe diameter is 14.1 cm. At location 1 the pipe is 8.03 m higher than it is at location 2. Ignoring viscosity, calculate the difference between the fluid pressure at location 2 and the fluid pressure at location 1.

Answer 1

Volume flow rate will be same throughout the pipe.

A1 v1 = A2 v2

(pi x (10.9/2)^2) (9.09) = ( pi x (14.1/2)^2) (v2)

v2 = 5.43 m/s

Now applying bernoulli's equation,

P + rho*g*h + rho * v^2 /2 = constant

P1 + (1110 x 9.8 x 8.03) + (1110 x 9.09^2/2) = P2 + (1110 x 9.8 x 0) + (1110 x 5.43^2 /2 )

P2 - P1 = 87350.34 + 555(9.09^2 - 5.43^2)   =116844.82 Pa