### Pressure Measurement

• Apply the principles of manometer to calculate pressure.

• Differentiate between absolute pressure and gauge pressure.

#### Piezometer Tube:

The direct proportional relation between gauge pressure and the height h for a fluid of constant density enables the pressure to be simply visualized in terms of the vertical height, $h = \frac{P}{\rho g}$

The height h is termed as pressure head corresponding to pressure p. For a liquid without a free surface in a closed pipe, the pressure head $\displaystyle h = \frac{P}{\rho g}$ at a point corresponds to the vertical height above the point to which a free surface would rise, if a small tube of sufficient length and open to atmosphere is connected to the pipe.

Such a tube is called a piezometer tube, and the height h is the measure of the gauge pressure of the fluid in the pipe. If such a piezometer tube of sufficient length were closed at the top and the space above the liquid surface were a perfect vacuum, the height of the column would then correspond to the absolute pressure of the liquid at the base. This principle is used in the well known mercury barometer to determine the local atmospheric pressure.

#### Barometer:

Barometer is used to determine the local atmospheric pressure. Mercury is employed in the barometer because its density is sufficiently high for a relative short column to be obtained. and also because it has very small vapour pressure at normal temperature. High density scales down the pressure head(h) to represent same magnitude of pressure in a tube of smaller height.

#### Manometers:

A manometer is also frequently used to measure the pressure difference, in course of flow, across a restriction in a horizontal pipe.

#### Inclined Tube Manometer:

For accurate measurement of small pressure differences by an ordinary u-tube manometer, it is essential that the ratio $\displaystyle \frac{r_{m}}{r_{w}}$ should be close to unity. This is not possible if the working fluid is a gas; also having a manometric liquid of density very close to that of the working liquid and giving at the same time a well defined meniscus at the interface is not always possible. For this purpose, an inclined tube manometer is used.

If the transparent tube of a manometer, instead of being vertical, is set at an angle $\displaystyle \theta$ to the horizontal, then a pressure difference corresponding to a vertical difference of levels x gives a movement of the meniscus s = x/sin q along the slope.

If $\displaystyle \theta$ is small, a considerable magnification of the movement of the meniscus may be achieved.

Angles less than 5$^\circ$ are not usually satisfactory, because it becomes difficult to determine the exact position of the meniscus.

#### Inverted Tube Manometer:

For the measurement of small pressure differences in liquids, an inverted U-tube manometer is used.

### Solved Example:

#### 61-2-01

Differential manometer is used to measure: (Based on JKSSB JE CE Oct 2021-Shift I)

Correct Answer: D

### Solved Example:

#### 61-2-02

Pitot tube is used for measurement of: (ISRO RAC 2017)

Correct Answer: C

### Solved Example:

#### 61-2-03

1 bar pressure is nearly equal to:

Solution:
1 bar = 1 $\times$ 10$^5$ N/m$^2$ $750\ mm\ Hg = 750 \times 10^{-3} \times 13600 \times 9.81 = 100062\ N/m^2$

Correct Answer: B

### Solved Example:

#### 61-2-04

Mercury is often used in barometer because: (Gujrat Engg Services 2017- Civil Part II)

Solution:

Mercury is much heavier than water (13.6 times) hence the column height required is only 760 mm as compared to 10.33m of water column. Also, it has very less vapor pressure hence the reading will be accurate. Mercury has in fact less viscosity, hence it is faster to react to the changes in pressure.

Correct Answer: D

### Solved Example:

#### 61-2-05

Barometer is used to measure: (CTET Sept 2014- Paper II)

Solution:
Barometer is used to measure atmospheric pressure. To measure difference of pressure between two points, U-tube manometer is used.

Correct Answer: B

### Solved Example:

#### 61-2-06

Select the correct statement:

Correct Answer: B

### Solved Example:

#### 61-2-07

Which of the following is correct?

Solution:
Absolute pressure is measured with reference to perfect vacuum, whereas gauge pressure is measured with reference to atmospheric pressure. Hence the difference between absolute pressure and gauge pressure is equal to atmospheric pressure.

Correct Answer: A

### Solved Example:

#### 61-2-08

The pressure in Pascals at a depth of 1 m below the free surface of a body of water will be equal to:

Solution:
$P = h \rho g = 1 \times 1000 \times 9.81 = 9810\ Pa$

Correct Answer: C

### Solved Example:

#### 61-2-09

The absolute pressure exerted on a diver at 30 m below the free surface of the sea will be :(Take barometric pressure = 101 kPa, specific weight of seawater = 10.3 $kN/m^3$

Solution:
$P = P_{atm} + h\rho g = 101 \times 10^3 + 30 \times 10.3\times 10^3 =\ 410\ kPa$

Correct Answer: A

### Solved Example:

#### 61-2-10

One of the differences between absolute pressure and gauge pressure is: (Prof. Prashant More's notes of Fluid Mechanics-II)

Solution:
Let us study these options individually.
Option A: Difference between gauge pressure and absolute pressure is the atmospheric pressure.
Option B: Absolute pressure can be positive or negative but gauge pressure can be positive or negative.
Option C: Already correct.
Option D: Gauge pressure is measured from atmospheric pressure whereas absolute pressure is measured from perfect vacuum.

Correct Answer: C

### Solved Example:

#### 61-2-11

A lake has maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 $N/m^3$, the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is: (GATE Civil 2021)

Solution:
Absolute pressure at the maximum depth of the lake \begin{align*} &= P_{atm} + \rho g h\\ &= 91 + \dfrac{9790 \times 60}{1000}\\ &= 678.4\ kPa \end{align*}

Correct Answer: B