---
title: "Oil-water manometer with gas cylinder"
subject: "Fluid Mechanics"
chapter: 2
key: "semester_3/fluid_mechanics:oil-water-manometer-gas-cylinder"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/oil-water-manometer-gas-cylinder
site: BCT Engineering
---

# Oil-water manometer with gas cylinder

Fluid Mechanics · Chapter 2: Pressure and Head

- Asked in: 2075 Chaitra, 8 marks
- Video: [U Tube Manometers - Pressure, Density & Height of Oil & Water - Fluid Mechanics](https://www.youtube.com/watch?v=0CKRGsLZh6Y) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/oil-water-manometer-gas-cylinder
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-2

## Question

An oil and water manometer consists of U-tube 4 mm diameter with both limbs vertical. The right-hand limb is enlarged at its upper end to 20 mm diameter. The enlarged end contains oil with its free surface in the enlarged portion and the surface of separation between water and oil is below the enlarged end. The left hand limb contains water only, its upper end being open to the atmosphere. When the right-hand side is connected to a cylinder of gas the surface of separation is observed to fall by 25 mm, but the surface of oil remains in the enlarged end. Calculate the gauge pressure in the cylinder. Assume that the specific gravity of the water is 1.0 and that of the oil 0.9.

## Short answer

Balancing pressures at the new interface after the 25 mm interface fall and 1 mm oil surface drop gives gauge pressure p = 278.6 Pa (≈0.28 kPa).

## Answer

**Data:** tube $d=4$ mm, enlarged end $D=20$ mm (right limb, oil above the interface), left limb water open to atmosphere. $s_w=1.0$, $s_o=0.9$. The interface falls $x=25$ mm. The gas pressure $p$ acts on the oil surface.

**Movement of the free surfaces**
- Left water surface rises $x=25$ mm (water pushed into the left limb of equal bore).
- Oil surface falls: $y=x\left(\dfrac{d}{D}\right)^{2}=25\left(\dfrac{4}{20}\right)^{2}=1$ mm.

Before the gas is connected both sides are open to the atmosphere and balanced at the initial interface level, so $\gamma_wH_w=\gamma_oH_o$. After the change, balance pressures at the new interface level ($x$ below the old):

$$
p+\gamma_o\,(H_o-y+x)=\gamma_w\,(H_w+x+x)
$$

Subtracting the initial balance:

$$
p=\gamma_w(2x)-\gamma_o(x-y)
$$

$$
p=9810(0.050)-0.9(9810)(0.025-0.001)
$$

$$
p=490.5-211.9=278.6\ \text{Pa}
$$

**Answer: gauge pressure in the cylinder $\approx278.6$ Pa (about 0.28 kPa, or 28 mm of water).**

## Check yourself

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

1. The interface falls 25 mm in the 4 mm limb. How far does the left water surface rise?
   A. 1 mm
   B. 25 mm
   C. 625 mm
   D. 50 mm
   Answer: B. The left limb has equal bore, so water rises by the same 25 mm. (Key point: Water surface movement)

2. How far does the oil surface fall in the 20 mm enlarged end?
   A. 25 mm
   B. 625 mm
   C. 5 mm
   D. 1 mm
   Answer: D. y = 25 (4/20)^2 = 1 mm. (Key point: Oil surface movement)

3. Which expression gives the gauge pressure?
   A. p = gamma_w (2x) - gamma_o (x - y)
   B. p = gamma_w x + gamma_o x
   C. p = gamma_w x - gamma_o y
   D. p = gamma_o (x + y)
   Answer: A. Balancing at the new interface level and subtracting the initial balance gives this result. (Key point: Pressure expression)

4. What is the gauge pressure?
   A. About 490 Pa
   B. About 279 Pa
   C. About 212 Pa
   D. About 2.8 kPa
   Answer: B. 490.5 - 211.9 = 278.6 Pa. (Key point: Final value)

## Related in Fluid Mechanics

- [Oil-water interface in enlarged-end U-tube](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Au-tube-enlarged-ends-oil-water-interface) — Fluid Mechanics, chapter 2
- [U-tube gauge with enlarged ends](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Au-tube-enlarged-ends-pressure-gauge) — Fluid Mechanics, chapter 2
- [Double U-tube manometer, oil and brine pipes](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Adouble-u-tube-oil-brine-pressure) — Fluid Mechanics, chapter 2

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