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 d1= 6.87 cm and d2= 2.15 cm, respectively.
The flow speed at location 1 is 2.71 m/s. What is the pressure difference, delta P between Location 2 and Location 1 (including its sign)? Ignore viscosity.

Answer 1

Density of the liquid = $\rho$ = 1330 kg/m³

Pressure of the liquid in the pipe at location 1 = P₁

Diameter of the pipe at location 1 = D₁ = 6.87 cm = 0.0687 m

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

Flow speed of the liquid in the pipe at location 1 = V₁ = 2.71 m/s

Pressure of the liquid in the pipe at location 2 = P₂

Diameter of the pipe at location 2 = D₂ = 2.15 cm = 0.0215 m

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

Flow speed of the liquid in the pipe at location 2 = V₂

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

By continuity equation,

A₁V₁ = A₂V₂

($\pi$D₁²/4)V₁ = ($\pi$D₂²/4)V₂

D₁²V₁ = D₂²V₂

(0.0687)²(2.71) = (0.0215)²V₂

V₂ = 27.67 m/s

The pipe is horizontal therefore location 1 and location 2 have same height.

By bernoulli's equation,

pVz = P2 P2+ 2 2

P2 P= 2. 2

P(VZ - V3) ДР-

(1330) (2.71)-(27.67)) Ρ- ΔΡ

$\Delta$P = -5.043 x 10⁵ Pa

Pressure difference between location 2 and location 1 = -5.043 x 10⁵ Pa