U Tube Manometer

Overview

Engineering reference data for U Tube Manometer in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Practical Examples

Example: Vertical U-Tube Manometer for Orifice Measurement

A water manometer connects the upstream and downstream pressure of an orifice located in an air flow. The difference in height in the water column is 10 mm.

The pressure difference head is calculated using the fundamental formula:

$p_d = \gamma h$

Substituting the values:

$p_d = (9.8 \, \text{kN/m}^3) \cdot (10^3 \, \text{N/kN}) \cdot (10 \, \text{mm}) \cdot (10^{-3} \, \text{m/mm}) = 98 \, \text{Pa}$

Example: Inclined U-Tube Manometer Measurement

Using the same differential pressure as above, but with the U-tube inclined at 45°. The measured length of the liquid column along the inclined tube is 10 mm.

The pressure difference for an inclined manometer is:

$p_d = \gamma h \sin(\theta)$

Substituting the values:

$p_d = (9.8 \, \text{kN/m}^3) \cdot (10^3 \, \text{N/kN}) \cdot (10 \, \text{mm}) \cdot (10^{-3} \, \text{m/mm}) \cdot \sin(45^\circ) = 69.3 \, \text{Pa}$

Key Considerations and Properties

Fluid Properties

The most common fluid used in U-tube manometers is water. Its specific weight ($\gamma$) is:

• SI Units: 9.81 kN/m³
• Imperial Units: 62.4 lb/ft³

Measurement Note

The pressure head unit (e.g., mm of water column) is defined with reference to the density of the fluid in the manometer tube, not the density of the fluid in the system being measured (e.g., air).

Accuracy Improvement with Inclined Manometers

A common challenge in low-velocity or low-density fluid systems (like air ducts) is that the vertical liquid column height ($h$) is very small, making accurate reading difficult.

• Solution: Inclining the U-tube manometer.
• Principle: By placing the tube at an angle ($\theta$) to the horizontal, the same pressure difference causes the liquid to travel a greater distance ($h$) along the tube's length.
• Result: This magnifies the displacement, improving the resolution and accuracy of the measurement. The actual pressure is calculated using $p_d = \gamma h \sin(\theta)$.

References

• Original Source