To double the flow rate at a nozzle, by what factor should the pressure be increased?

To double the flow rate at a nozzle, by what factor should the pressure be increased?

• A. Increase the pressure by 2X
• B. Increase the pressure by 4X
• C. Increase the pressure by 10X
• D. Increase the pressure by 0.5X

Answer: (B)

In a nozzle, flow rate is tied to how pressure difference turns into velocity. For an ideal, frictionless nozzle with incompressible flow, the velocity scales with the square root of the pressure drop: v ∝ sqrt(ΔP). The flow rate Q is the velocity times the cross-sectional area, so Q ∝ sqrt(ΔP) as well. To get twice as much flow (Q doubles), the pressure drop must increase by the square of that factor: (ΔP2/ΔP1) = 2^2 = 4. So the pressure needs to be increased by a factor of four. In real systems, losses and compressibility can alter this, but under the common assumptions this quadruple pressure gives double the flow.

In a nozzle, flow rate is tied to how pressure difference turns into velocity. For an ideal, frictionless nozzle with incompressible flow, the velocity scales with the square root of the pressure drop: v ∝ sqrt(ΔP). The flow rate Q is the velocity times the cross-sectional area, so Q ∝ sqrt(ΔP) as well. To get twice as much flow (Q doubles), the pressure drop must increase by the square of that factor: (ΔP2/ΔP1) = 2^2 = 4. So the pressure needs to be increased by a factor of four. In real systems, losses and compressibility can alter this, but under the common assumptions this quadruple pressure gives double the flow.