---
title: "Force of jet on flat plate, stationary and moving"
subject: "Fluid Machines"
chapter: 1
key: "semester_5/fluid_machines:jet-on-flat-plate-numerical"
source: https://www.bctengineer.com/q/semester_5/fluid_machines/jet-on-flat-plate-numerical
site: BCT Engineering
---

# Force of jet on flat plate, stationary and moving

Fluid Machines · Chapter 1: Introduction of Turbomachime and Dynamic Action of Fluid

- Asked in: year not given, 8 marks
- Video: [Fluid Machinery lecture 1: Impact of jets, force on curved and flat plate.](https://www.youtube.com/watch?v=rxxP7bu1dN0) — Mech Zone
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/fluid_machines/jet-on-flat-plate-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_5/fluid_machines/chapter-1

## Question

A jet of water 50 mm in diameter with a velocity of 25 m/s strikes a flat plate held normal to the jet. Find (a) the force on the plate when it is stationary, (b) the force, work done per second and efficiency of the jet when the plate moves at 8 m/s in the direction of the jet (single plate), and (c) the same quantities when a series of such plates mounted on a wheel moves at 8 m/s.

## Short answer

(a) Stationary plate: F = ρaV² = 1227.2 N. (b) Single moving plate: relative velocity (V-u), mass flow ρa(V-u), F = ρa(V-u)² = 567.5 N, work = Fu = 4540 W, efficiency = 29.6%. (c) Series of plates: full mass flow ρaV, F = ρaV(V-u) = 834.5 N, work = 6676 W, efficiency = 43.5%.

## Answer

**Given:** $d = 0.05$ m, $V = 25$ m/s, $u = 8$ m/s, $\rho = 1000$ kg/m³.

Jet area: $a = \frac{\pi}{4}(0.05)^2 = 1.9635\times10^{-3}$ m².

Kinetic energy of jet per second (input power): $\frac12\rho a V^3 = 15340$ W.

#### (a) Stationary plate

The jet loses all its momentum normal to the plate.

$$
F = \rho a V^2 = 1000\times 1.9635\times10^{-3}\times 25^2 = 1227.2\ \text{N}
$$

#### (b) Single plate moving at 8 m/s

Only the relative velocity $(V-u)$ acts, and the mass hitting the plate per second is $\rho a (V-u)$ (the plate runs away from the jet, so some water is not caught).

$$
\begin{aligned}
F &= \rho a (V-u)^2 = 1000\times1.9635\times10^{-3}\times 17^2 = 567.5\ \text{N}\\
W &= F\,u = 567.5\times 8 = 4540\ \text{W}\\
\eta &= \frac{F u}{\tfrac12\rho a V^3} = \frac{4540}{15340} = 29.6\%
\end{aligned}
$$

#### (c) Series of plates on a wheel

With many plates, a plate is always in front of the jet, so the whole discharge $\rho a V$ strikes the plates, but each kilogram loses only the relative velocity $(V-u)$.

$$
\begin{aligned}
F &= \rho a V (V-u) = 1000\times1.9635\times10^{-3}\times25\times 17 = 834.5\ \text{N}\\
W &= F u = 6676\ \text{W}\\
\eta &= \frac{2u(V-u)}{V^2} = \frac{6676}{15340} = 43.5\%
\end{aligned}
$$

The maximum efficiency of a series of flat plates is 50 %, at $u = V/2$.

| Case | Force (N) | Work (W) | Efficiency |
|---|---|---|---|
| Stationary | 1227.2 | 0 | 0 |
| Single moving plate | 567.5 | 4540 | 29.6 % |
| Series of plates | 834.5 | 6676 | 43.5 % |

**Answer:** (a) 1227.2 N; (b) 567.5 N, 4540 W, 29.6 %; (c) 834.5 N, 6676 W, 43.5 %.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The force of the jet on the stationary plate is found from:
   A. 0.5 rho a V^3
   B. rho a (V-u)^2
   C. rho a V (V-u)
   D. rho a V^2
   Answer: D. The jet loses all normal momentum: F = rho a V^2 = 1227.2 N. (Key point: Stationary plate)

2. For a single plate moving at u, the mass striking the plate per second is:
   A. rho a (V-u)
   B. rho a V
   C. rho a (V+u)
   D. rho a u
   Answer: A. The plate runs away so only rho a (V-u) is caught; F = rho a (V-u)^2 = 567.5 N. (Key point: Single moving plate)

3. For a series of plates on a wheel, the force is rho a V (V-u) because:
   A. Only the relative flow hits the plate
   B. Velocity doubles
   C. The whole discharge rho a V strikes the plates, each kg losing velocity (V-u)
   D. The plates are stationary
   Answer: C. A plate is always in front of the jet, so full discharge is used; each kg loses (V-u). (Key point: Series of plates)

4. Maximum efficiency of a series of flat plates and the speed at which it occurs:
   A. 50% at u = V/2
   B. 100% at u = V
   C. 29.6% at u = V/2
   D. 43.5% at u = V/3
   Answer: A. eta = 2u(V-u)/V^2 is maximum, 50%, at u = V/2. (Key point: Maximum efficiency)

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