What nozzle reaction does a 32mm tip with 350 kPa nozzle pressure produce?

• A. 538 kPa
• B. 400 kPa
• C. 600 kPa
• D. 320 kPa

Answer: (A)

Nozzle reaction is the thrust the nozzle experiences from the water flowing through it. For a smooth-bore nozzle discharging into atmosphere, a handy way to estimate the reaction is to account for both the pressure pushing the water out and the momentum carried by the exiting jet. The combined effect leads to NR ≈ 3 p A, where p is the nozzle pressure and A is the nozzle exit area. This captures the pressure thrust (p × A) plus the momentum thrust (ṁ × v), with the relationship v^2 ≈ 2p/ρ making the momentum term contribute an amount roughly equal to 2p when expressed in the appropriate form, giving the factor of 3 when combined with the pressure term.

Calculate the exit area: with a 32 mm diameter tip, D = 0.032 m, A = πD^2/4 = π(0.032)^2/4 ≈ 0.000804 m^2.

Using p = 350 kPa = 350,000 Pa:

NR = 3 p A ≈ 3 × 350,000 × 0.000804 ≈ 844 N.

If you express this nozzle reaction as an equivalent pressure over the nozzle exit area, NR/A ≈ 844 / 0.000804 ≈ 1,050,000 Pa = 1050 kPa.

So the nozzle reaction for a 32 mm tip at 350 kPa nozzle pressure is about 1050 kPa (the reaction force on the nozzle is roughly 0.84 kN). The key idea is that the nozzle reaction is greater than the nozzle pressure because it includes both the pressure thrust and the momentum thrust of the exiting water.