Test: Pressure Measuring Devices - Civil Engineering (CE) MCQ

Hydrostatic Law:

It states that the rate of increase of pressure in a vertical direction is equal to the weight density of the fluid at that point.

P = ρgh
Calculation:
Given:

Pressure at point A = 0.2 × 800 × 9.81 = 1.569 kPa
Pressure at Point B = 0.42 × 1000 × 9.81 = 4.12 kPa
PA + y × 0.8 × 9.81 + x × 9.81 = PB [x & y in metre]
0.8 y + x = 0.26
& x + y = 0.3
solving both equation
x = 0.1 m = 10 cm

Bourdon Tube:

• Bourdon gauges are available to cover a large range of pressures.
• Bourdon gauges are purely mechanical devices utilizing the mechanical deformation of a flattened but bent tube that winds or unwinds depending on the pressure difference between the inside and the outside.
• The motion is against a spring torque such that a needle attached to the shaft indicates directly the pressure difference.
  
  Bourdon tube pressure gauges are the most common type in many areas and are used to measure medium to high pressures. They cover measuring spans from 600 mbar to 4,000 bar. The measuring element is a curved tube with a circular, spiral or coiled shape, commonly called a bourdon tube.

Manometer:
A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and another end remains open to the atmosphere. Common types of simple manometers are:

• Piezometer
• U-tube Manometer
• Single Column Manometer

Differential Manometers measure the difference in pressure between two points in a fluid system and cannot measure the actual pressures at any point in the system. It consists of a U-tube, containing a heavy liquid, whose two ends are connected to the points whose difference in pressure is to be measured.

Given:
ρ₁ = Specific gravity of mercury =  13.6, ρ₂ =Specific gravity of kerosene =  0.8, h= 40 cm  

Let h₁ on the left side be the level of mercury, before pouring of kerosene

After pouring kerosene, 40 cm height is taken by kerosene, mercury is lowered by h₁ on the left side and mercury on the right side raises by h₁ from its original position, ie when kerosene was not poured 
ρ₁ = 13.6, ρ₂ = 0.8, h= 40 cm 
Writing the pressure equation for the above diagram, according to the final location of the mercury and kerosene, we get
40 × G for kerosene - 2 × h₁ × G for mercury = 0, (pressure at level B and B^' is the same, as they are at the same level)
40 × 0.8 = 2 × h₁ × 13.6
h₁ = 1.17 cm ≈ 1.2 cm

Concept:
In an open tube manometer

• The pressure at both the open ends is atmospheric.
• The pressure at any point inside the column can be calculated from either side.

Calculation:
Given:

ρ_water = 1000 kg/m³, l = 80 mm and d = 20 mm
So, the pressure at the bottom of the oil column can be equated from either end to find the required value of ρoil
ρoil × g × (d + l) = ρwater × g × l
ρoil × (20 + 80) = 1000 × 80
ρoil = 800 kg/m³
Hence the required density of oil is 800 kg/m³.

Force balance: Use for calibration of pressure measuring instruments
Barometer: Atmospheric pressure is measured by a device called a barometer; thus, the atmospheric pressure is often referred to as the barometric pressure.
P_atm = ρgh
Where, ρ = Density, g = local gravitational acceleration, h = height of the mercury column above the free surface.
Frequently use standard atmospheric pressure unit is,
P_atm = 760 mm of Hg column = 10.3 m of H₂O column

 

Mechanical gauge: It is a device used for measuring the gauge pressure by balancing the spring balance or dead weight. The commonly use mechanical pressure gauges are,

• Diaphragm pressure gauge
• Bourdon pressure gauge
• Deadweight pressure gauge
• Bellows pressure gauge

Single column manometer:

(i) Single column manometer is a modified form of a U-tube manometer in which one side is a large reservoir and the other side is a small tube, open to the atmosphere.
There are two types of single-column manometer:

• Vertical single-column manometer.
• Inclined single-column manometer.

Vertical single column manometer:

 

Inclined single column manometer:
This manometer is more sensitive. Due to the inclination, the distance moved by the heavy liquid in the right limb will be more.

Inclined column manometer: 

• In an inclined column manometer the column is inclined at some angle with the horizontal axis.
• Due to inclination, the distance moved by the heavy liquid in the right limb is more.
• This manometer is more sensitive. 
  
• The sensitivity of the inclined manometer is given by 1/sin⁡θ
• The inclined manometer is used for measuring the actual airflow and is simply a more sensitive way of using a manometer, what is of interest is still the height the fluid moves up vertically.

Concept:
The barometer is an instrument used to measure the pressure of air. There are two typed of barometers, the mercury manometer and, aneroid barometer.
Mercury barometer: In a mercury barometer a tube filled with mercury is placed upright with its open end down into a container of more mercury.
Air pressure on the mercury in the container keeps the mercury from draining out of the tube.
Aneroid barometer: An aneroid barometer uses a flexible metal bellows instead of mercury to measure air pressure.
Calculation:
The gauge pressure = P_abs - P_atm
At atmospheric pressure the gauge pressure = 0

Now if we write the equation for pressure in vertical column then,
P_atm – ρ_m × g × h – P_vapour = 0
⇒ P_atm = ρ_m × g × h + P_vapour
Now Since At atmospheric pressure the gauge pressure = 0
(P_vapour­)_gauge = -ρ_m × g × h
∴ Gauge pressure of vapour will be negative.

U-tube Manometer:
(i) It consists of a glass tube in U shape, one end of which connected to the gauge point and another end open to the atmosphere.
(ii) The tube contains a liquid of specific gravity greater than that of the fluid of which the pressure is to be measured.
(iii) The choice of the manometric liquid depends on the range of pressure to be measured For the low-pressure range, liquid of lower SG is used and for the high range, generally, mercury is used.
(iv) A U-tube manometer is used inverted if the pressure differential is small (density of the manometric fluid is less than fluid) and A U-tube manometer is used upright if the pressure differential is large (density of the manometric fluid is large)
Limitation:

• This method requires reading of fluid level at two or more points since the change in pressure causes a rise in one limb and drop in another.