---
title: "Zero pressure difference under upward acceleration"
subject: "Fluid Mechanics"
chapter: 2
key: "semester_3/fluid_mechanics:upward-acceleration-pressure-difference"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/upward-acceleration-pressure-difference
site: BCT Engineering
---

# Zero pressure difference under upward acceleration

Fluid Mechanics · Chapter 2: Pressure and Head

- Asked in: 2079 Baisakh, 4 marks
- Video: [Class 11 Physics | Fluid Statics | #19 Pressure Distribution in an Accelerated Frame |For JEE & NEET](https://www.youtube.com/watch?v=XCR4dDUDJqE) — Physics Galaxy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/upward-acceleration-pressure-difference
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-2

## Question

A water body is subjected to an acceleration in the vertically upward direction. At what acceleration will the pressure difference between two points, separated by a vertical distance h, be zero?

## Short answer

The pressure difference between two points distance h apart under vertical acceleration a_z is Δp = ρh(g + a_z). Setting Δp = 0 requires a_z = –g (free fall). For any upward acceleration, Δp > ρgh and can never be zero.

## Answer

**Answer: the pressure difference becomes zero only when the whole water body has a *downward* acceleration equal to $g$ (free fall), i.e. $a_z=-g$. For any upward acceleration it can never be zero; it only increases.**

Take a fluid element in a body moving with vertical acceleration $a_z$ (upward positive). Newton's second law for a column of height $h$ and unit area:

$$
p_2A-p_1A-\rho g h A=\rho h A\,a_z
$$

where point 1 is the upper point and point 2 the lower point, a distance $h$ apart. So

$$
\Delta p=p_2-p_1=\rho h\,(g+a_z)
$$

Setting $\Delta p=0$:

$$
g+a_z=0\ \Rightarrow\ a_z=-g
$$

For an upward acceleration $a_z>0$, $\Delta p=\rho h(g+a_z)>\rho g h$, so the pressure difference is greater than the static value. At free fall (weightless condition) the fluid has no apparent weight and the pressure is uniform throughout.

## Check yourself

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

1. For a fluid with vertical acceleration a_z (upward positive), what is the pressure difference over height h?
   A. rho h (g - a_z)
   B. rho g h
   C. rho h (g + a_z)
   D. rho h a_z
   Answer: C. Newton's law gives Delta p = rho h (g + a_z). (Key point: Pressure difference formula)

2. At what acceleration does the pressure difference become zero?
   A. Upward acceleration equal to g
   B. Downward acceleration equal to g (free fall)
   C. Upward acceleration equal to 2g
   D. Zero acceleration
   Answer: B. g + a_z = 0 gives a_z = -g, i.e. free fall. (Key point: Zero pressure difference condition)

3. What happens to the pressure difference for any upward acceleration?
   A. It is less than rho g h
   B. It becomes zero
   C. It becomes negative
   D. It is greater than rho g h
   Answer: D. Delta p = rho h (g + a_z) > rho g h when a_z > 0. (Key point: Upward acceleration effect)

4. What is the state of the fluid in free fall?
   A. It has no apparent weight and pressure is uniform
   B. It has double weight
   C. Pressure increases with depth faster
   D. It cannot exist
   Answer: A. The fluid is weightless, so no hydrostatic variation occurs. (Key point: Free-fall meaning)

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