A sudden valve closure in a pipe of fluid with density 1000 kg/m^3 and wave speed a = 1000 m/s and initial velocity V = 2 m/s. If ΔV = 2 m/s, compute maximum surge pressure ΔP using ΔP = ρ a ΔV.

• A. 1.0×10^6 Pa
• B. 2.0×10^6 Pa
• C. 3.0×10^6 Pa
• D. 4.0×10^6 Pa

Answer: (B)

When a valve closes suddenly, the moving fluid cannot stop instantaneously, creating a pressure surge known as water hammer. The maximum surge pressure for a rapid change in velocity in a long, elastic pipe is given by ΔP = ρ a ΔV, where ρ is the fluid density, a is the wave (celerity) speed of pressure waves in the fluid, and ΔV is the change in fluid velocity.

Plugging in the values: ρ = 1000 kg/m^3, a = 1000 m/s, and ΔV = 2 m/s gives ΔP = 1000 × 1000 × 2 = 2,000,000 Pa = 2 MPa.

The initial velocity being 2 m/s means the velocity drops by 2 m/s when the valve closes, which is exactly the ΔV used in the formula. Therefore, the maximum surge pressure is 2.0×10^6 Pa.