---
title: "Jet from tank on plate over second tank"
subject: "Fluid Mechanics"
chapter: 7
key: "semester_3/fluid_mechanics:two-tanks-jet-plate-height"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/two-tanks-jet-plate-height
site: BCT Engineering
---

# Jet from tank on plate over second tank

Fluid Mechanics · Chapter 7: Momentum principle and flow analysis

- Asked in: 2076 Chaitra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/two-tanks-jet-plate-height
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-7

## Question

Two large tanks containing water have small smoothy orifices of equal area. A jet of liquid issues from the left tank. Assume the flow is uniform and unaffected by friction. The jet impinges on the vertical flat plate covering the opening of the right tank. Determine the minimum value for height, h, required to keep the plate in place over the opening of the right tank. [Figure: left tank with water head h above its orifice; right tank with constant head H; jet of liquid from left orifice hitting a plate over the right orifice]

## Short answer

Minimum head h is H/2. The jet force 2ρg a h balances the water pressure force ρg a H on the right orifice plate.

## Answer

**Setup:** The left tank has water head $h$ above its orifice; the right tank has head $H$ above its orifice (water depth in the right tank is large and constant). Both orifices have equal area $a$. The plate covers the right orifice and is kept in place only by the jet.

#### Force of the jet

By Torricelli's theorem, the jet speed is $V = \sqrt{2gh}$. The jet strikes the vertical plate normally and loses all its horizontal momentum:

$$
F_{jet} = \rho aV^2 = \rho a(2gh) = 2\rho g\,a\,h
$$

(If the jet area is $a$ at the vena contracta, the same expression applies for small smooth orifices.)

#### Force from the water in the right tank

The water pressure acts on the plate covering the orifice, trying to push it away. Taking the pressure at the orifice (small area) as $\rho gH$:

$$
F_{water} = \rho g\,H\,a
$$

#### Condition to keep the plate in place

$$
F_{jet} \ge F_{water}\;\Rightarrow\; 2\rho g\,ah \ge \rho g\,aH\;\Rightarrow\; h \ge \frac{H}{2}
$$

**Answer: the minimum height is $h_{min} = H/2$**, i.e. the head in the left tank must be at least half of the head in the right tank.

## Check yourself

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

1. What is the jet speed from the left tank?
   A. sqrt(2gH)
   B. sqrt(gh)
   C. sqrt(2gh)
   D. 2gh
   Answer: C. By Torricelli's theorem. (Key point: Jet speed)

2. What force does the jet apply to the plate?
   A. rho a sqrt(2gh)
   B. rho a g H
   C. rho g a h
   D. rho a (2gh) = 2 rho g a h
   Answer: D. Rate of momentum loss rho a V^2 with V^2 = 2gh. (Key point: Jet force)

3. What force acts on the plate from the right tank water?
   A. rho g H a
   B. zero
   C. 2 rho g H a
   D. rho g a h
   Answer: A. Pressure rho g H acts on the orifice area a. (Key point: Opposing force)

4. What is the minimum h?
   A. H/4
   B. H/2
   C. H
   D. 2H
   Answer: B. 2 rho g a h >= rho g a H gives h >= H/2. (Key point: Result)

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