Question

A liquid of density 1.33 × 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 14.3 cm. At location 1 the pipe is 9.75 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

Gravitational acceleration = g = 9.81 m/s²

Density of the liquid = = 1.33 x 10³ kg/m³

Fluid pressure in the pipe at location 1 = P₁

Diameter of the pipe at location 1 = D₁ = 10.9 cm = 0.109 m

Cross-sectional area of the pipe at location 1 = A₁ = D₁²/4

Speed of flow of fluid at location 1 = V₁ = 9.09 m/s

Fluid pressure in the pipe at location 2 = P₂

Diameter of the pipe at location 2 = D₂ = 14.3 cm = 0.143 m

Cross-sectional area of the pipe at location 2 = A₂ = D₂²/4

Speed of flow of fluid at location 2 = V₂

Height of location 1 compared to location 2 = H = 9.75 m

Fluid pressure difference at location 2 and location 1 = P = P₂ - P₁

By continuity equation at location 1 and 2,

A₁V₁ = A₂V₂

(D₁²/4)V₁ = (D₂²/4)V₂

D₁²V₁ = D₂²V₂

(0.109)²(9.09) = (0.143)²V₂

V₂ = 5.28 m/s

By Bernoulli's equation at location 1 and 2,

P = 1.636 x 10⁵ Pa

Fluid pressure difference at location 2 and location 1 = 1.636 x 10⁵ Pa