---
title: "U-tube manometer with oil, mercury and water"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:u-tube-oil-mercury-water"
source: https://www.bctengineer.com/q/semester_6/hydro_power/u-tube-oil-mercury-water
site: BCT Engineering
---

# U-tube manometer with oil, mercury and water

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2080 Asoj, 6 marks
- Video: [Pressure Measurement Manometers](https://www.youtube.com/watch?v=oXXGIFSmZRE) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/u-tube-oil-mercury-water
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

A U-tube manometer contains oil, mercury, and water as shown in figure below. For the column heights indicated, what is the pressure differential between pipe A and B? [Figure: pipe A (oil, SG = 0.9) on the left and pipe B (water) on the right are connected by a U-tube with mercury (SG = 13.6) at the bottom; the column heights marked are 4 cm, 3 cm and 12 cm.]

## Short answer

Manometer equation: p_A + 0.9×9810×0.12 − 13.6×9810×0.04 − 9810×0.03 = p_B. Compute: p_A − p_B = 9810(0.544+0.03−0.108) = 4571 Pa ≈ 4.57 kN/m², A higher.

## Answer

Use the manometer rule: start at A, add $\rho g h$ when going down a column, subtract when going up, and end at B.

**Assumed reading of the figure:** A (oil) is 12 cm above the oil–mercury surface in the left limb. Mercury in the right limb stands 4 cm higher than in the left limb. B (water) is 3 cm above the right mercury surface.

**Given:** oil $S = 0.9$, mercury $S = 13.6$, water $S = 1$; $\rho_w g = 9810$ N/m³.

```text
  A (oil)
  |                         B (water)
  | 12 cm oil               | 3 cm water
  |              Hg  -------+ (right Hg level)
  |              | 4 cm
  +-- Hg level --+
  |_____ mercury ______|
```

#### Manometer equation
$$
p_A + \rho_{oil} g(0.12) - \rho_{Hg} g(0.04) - \rho_w g(0.03) = p_B
$$
$$
\begin{aligned}
p_A - p_B &= 9810\,[13.6(0.04) + 1(0.03) - 0.9(0.12)] \\
&= 9810\,[0.544 + 0.030 - 0.108] \\
&= 9810 \times 0.466 = 4571\ \text{N/m}^2
\end{aligned}
$$

**Answer:** $p_A - p_B \approx 4.57$ kN/m² (pressure at A is higher). If the column heights are arranged differently in the figure, the same step-by-step balance applies with those heights.

## Check yourself

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

1. Moving through a manometer from A to B, pressure:
   A. Increases going up a column, decreases going down
   B. Increases going down a column, decreases going up
   C. Is unchanged
   D. Changes only in mercury
   Answer: B. Add rho g h when going down and subtract when going up. (Key point: Manometer rule)

2. The equation used is:
   A. p_A + rho_oil g(0.12) - rho_Hg g(0.04) - rho_w g(0.03) = p_B
   B. p_A - rho_oil g(0.12) + rho_Hg g(0.04) + rho_w g(0.03) = p_B
   C. p_A + rho_oil g(0.12) + rho_Hg g(0.04) + rho_w g(0.03) = p_B
   D. p_A = p_B
   Answer: A. Down 12 cm oil (+), up 4 cm mercury (-), up 3 cm water (-). (Key point: Equation)

3. p_A - p_B = 9810[13.6(0.04) + 1(0.03) - 0.9(0.12)]. The bracket equals:
   A. 0.466
   B. 0.682
   C. 0.574
   D. 1.2
   Answer: A. 0.544 + 0.030 - 0.108 = 0.466. (Key point: Bracket)

4. The pressure difference p_A - p_B is about:
   A. 0.466 kN/m^2
   B. 4.57 kN/m^2
   C. 45.7 kN/m^2
   D. 9.81 kN/m^2
   Answer: B. 9810 x 0.466 = 4571 N/m^2 = 4.57 kN/m^2. (Key point: Result)

## Related in Hydro Power

- [Differential manometer pressure at point B](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-air-water-oil) — Hydro Power, chapter 1
- [Differential manometer between CCl4 and oil pipes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-ccl4-oil-pipes) — Hydro Power, chapter 1
- [Manometer between oil and water pipes](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-oil-water-pipes) — Hydro Power, chapter 1
- [Pressure difference using compound manometer](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-water-oil-mercury) — Hydro Power, chapter 1
- [Pressure difference between containers A and B](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Amanometer-inclined-containers) — Hydro Power, chapter 1

## Related in other subjects

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