Question 7 of 13: Jet Force on a Plate: Dynamic vs. Static

Question 7 — Jet Force on a Plate: Dynamic vs. Static (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. (a) the force from the free jet striking a plate held away from the nozzle; (b) the static force when the plate blocks the nozzle (no flow); and whether they are equal.

Approach. Part (a) uses the momentum equation on the free jet (the plate turns the flow through 90°, so the full axial momentum is destroyed); part (b) is simple hydrostatics since there is no flow.

1. Part (a) — jet velocity and momentum force. $$V=\sqrt{{2gh}}=\sqrt{{2\times9.81\times2}}=6.26\text{{ m/s}},\quad A=\frac{{\pi}}{{4}}(0.030)^2=7.069\times10^{{-4}}\text{{ m}}^2$$ $$Q=AV=7.069\times10^{{-4}}\times6.26=4.43\times10^{{-3}}\text{{ m}}^3/\text{{s}}$$ $$F_{{jet}} = \rho Q V = 1000\times4.43\times10^{{-3}}\times6.26 = \boxed{{27.7\text{{ N}}}}$$
2. Part (b) — static pressure force. $$p=\rho g h = 1000\times9.81\times2 = 19,620\text{{ Pa}}$$ $$F_{{static}} = pA = 19,620\times7.069\times10^{{-4}} = \boxed{{13.9\text{{ N}}}}$$
3. Comparison. $$\frac{{F_{{jet}}}}{{F_{{static}}}}=\frac{{\rho A V^2}}{{\rho g h A}}=\frac{{V^2}}{{gh}}=\frac{{2gh}}{{gh}}=2.00$$ The two forces are not the same — the dynamic jet force is exactly twice the static pressure force, independent of the specific numbers, because the moving jet carries kinetic energy (V²=2gh) on top of having already converted the full head to velocity, while the static case only ever develops the pressure head itself.