Define the cavitation number sigma and its relation to NPSH and vapor pressure.

• A. σ = (p1 − p_v) / (0.5 ρ v^2) or, in suction use, σ = (p_atm − p_v) / (ρ g H); lower σ indicates higher cavitation risk; relates available pressure head to vapor pressure
• B. σ = (p1 − p_v) / (ρ g H)
• C. σ = p_atm / p_v
• D. σ = ΔP / (ρ v^2)

Answer: (A)

The cavitation number measures how close the liquid is to cavitation by comparing the pressure margin above the vapor pressure to the flow’s dynamic head. It can be written as σ = (p1 − pv) / (0.5 ρ v^2), where p1 is the pressure at the pump inlet and pv is the vapor pressure. On suction, this becomes σ = (p_atm − pv) / (ρ g H), where p_atm is the atmospheric pressure and H is the velocity head (H = v^2/(2g)). These forms are equivalent because ρ g H equals 0.5 ρ v^2.

A small σ means the available margin above pv is small compared with the flow’s kinetic energy, so cavitation risk is high. Conversely, a larger σ indicates a bigger margin and lower risk. This ties directly to NPSH: the available suction head above vapor pressure (NPSHa) represents that margin, and cavitation occurs when NPSHa is not sufficient to meet the pump’s requirements (NPSHr). So σ effectively normalizes the pressure margin by the flow’s head, linking vapor pressure, available pressure, and velocity.