A liquid of density 129 103 kgm3 flows steadily through a p

A liquid of density 1.29 × 103 kg/m3 flows steadily through a pipe of varying diameter and height. At location 1 along the pipe the flow speed is 9.35 m/s and the pipe diameter is 1.15 × 101 cm. At location 2 the pipe diameter is 1.59 × 101 cm. At location 1 the pipe is 9.61 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 in Pa

Solution

Volume flow rate of fluid will be same throughout the pipe.

A1 v1 = A2 v2

pi (1.15 x 10 / 2)^2 (9.35) = pi (1.59 x 10 /2)^2 v2

v2 = 4.89 m/s

Applying Bernoulli\'s equation,

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

at 1 =at 2

P1 + (1290 * 9.81 * 9.61) + (1290 * 9.35^2 /2 ) = P2 + (0 ) + (1290 x 4.89^2 /2 )

P1 + 121613.6 + 56387.5 =P2 + 15423.3

P2 - P1 = 162577.8 Pa