Question

A horizontal pipe carries a smoothly flowing liquid of density of 1330 kg/m3. At Locations 1 and 2 along the pipe, the diameters are ?1=5.71 cm and ?2=2.33 cm, respectively. The flow speed at Location 1 is 2.07 m/s . What is the pressure difference Δ? between Location 2 and Location 1 (including its sign)? Ignore viscosity.

Answer 1

Density of fluid = = 1330 kg/m³

Pressure at location 1 = P₁

Pressure at location 2 = P₂

Diameter of pipe at location 1 = d₁ = 5.71 cm = 0.0571 m

Diameter of pipe at location 2 = d₂ = 2.33 cm = 0.0233 m

Speed of flow at location 1 = V₁ = 2.07 m/s

Speed of flow at location 2 = V₂

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

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

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

By continuity equation,

A₁V₁ = A₂V₂

(d₁²/4)V₁ = (d₂²/4)V₂

V₁d₁² = V₂d₂²

(2.07)(0.0571)² = V₂(0.0233)²

V₂ = 12.43 m/s

The pipe is horizontal, hence there is no height difference between locations 1 and 2.

By bernoulli's equation,

P₁ + V₁²/2 = P₂ + V₂²/2

P₂ - P₁ = (V₁² - V₂²)/2

P = (1330)[(2.07)² - (12.43)²]/2

P = - 99896.3 Pa

Pressure difference between location 2 and location 1 = - 99896.3 Pa