Question

A liquid of density 1270 kg/m31270 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.61 m/s9.61 m/s and the pipe diameter ?1d1 is 10.7 cm10.7 cm. At Location 2, the pipe diameter ?2d2 is 16.1 cm16.1 cm. At Location 1, the pipe is Δ?=8.31 mΔy=8.31 m higher than it is at Location 2. Ignoring viscosity, calculate the difference Δ?ΔPbetween the fluid pressure at Location 2 and the fluid pressure at Location 1.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of liquid = = 1270 kg/m³

Pressure at location 1 = P₁

Speed of flow at location 1 = V₁ = 9.61 m/s

Diameter of pipe at location 1 = d₁ = 10.7 cm = 0.107 m

Area of pipe at location 1 = A₁ = d₁²/4

Pressure at location 2 = P₂

Speed of flow at location 2 = V₂

Diameter of pipe at location 2 = d₂ = 16.1 cm = 0.161 m

Area of pipe at location 2 = A₂ = d₂²/4

At location 1 the pipe is 8.31m higher than at location 2.

y = 8.31 m

Pressure difference at location 2 and 1 = P = P₂ - P₁

By continuity equation,

A₁V₁ = A₂V₂

(d₁²/4)V₁ = (d₂²/4)V₂

d₁²V₁ = d₂²V₂

(0.107)²(9.61) = (0.161)²V₂

V₂ = 4.244 m/s

By applying Bernoulli's equation,

P = 150738.05 Pa

P = 1.507 x 10⁵ Pa

The difference between the fluid pressure at location 2 and the fluid pressure at location 1 = 1.507 x 10⁵ Pa