U-Tube Manometer - Free MCQ Practice Test with solutions, GATE Civil Fluid

Concept:
U-tube Manometer:

• It is a transparent glass tube bent in a U shape initially both ends are open to the atmosphere after that one end of the U-tube is connected to the point at which the pressure of the liquid is to be measured and another end is open to the atmosphere.
• The U-tube is filled with the manometric fluid whose Specific gravity should be higher than the liquid whose pressure is to be measured. initially, the level of the manometric fluid will be same in the both of the limbs.

U-tube manometer for gauge pressure:

•  to calculate the gauge pressure let at point P, you may simply use the hydrostatic law and balance the column concepts So the pressure at the point P will be;
• P_A = ρ₁gh₁ - ρ₂gh₂
• here, h₂ and h₁ height of the right and left limbs above the reference line X-X.
• The absolute pressure at point A, Pabsolute = P_A + Patm

Calculation:
Given:

P_absolute = P_atm + ρwgh1 + ρ_Hggh2 - ρwgh3 
where,  Patm = 101.32 kPa, ρ = 1000 Kg/m³ , ρHg = 13600  Kg/m³, h₁ = 0.05 m, h₂ = 0.02 m, h₃ = 0.17 m.
P_absolute = 101.32 × 1000 + 1000 × 9.81 × 0.05 + 13600 × 9.81 × 0.02 - 1000 × 9.81 × 0.17
P_absolute = 102887.28 Pa
Head in terms of Hg column is given by:
h_Hg  × ρ_Hg × g = Pabsolute 
h_Hg × ρ_Hg × g = 102887.28
h_Hg = 771.17 mm

Concept:
Differential Manometers:

• Differential manometers are devices used for measuring the difference of pressures between two points in a pipe or in two different pipes.
• A differential manometer consists of a U-tube, containing a heavy or light liquid, whose two ends are connected to the points, whose difference of pressure is to be measured.
• The most common types of differential manometers are

1. U-tube differential manometer
2. Inverted U-tube differential manometer

• The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured.

U-tube differential manometer

• It consists of a U-tube containing a heavy liquid. 
• The two ends of the tube are connected to the points whose difference is to be measured. 
• It is used for measuring the difference of pressure between two points in the flow section to which it is connected.

Differential inverted U-tube manometer: 

• It consists of an inverted U-tube containing a light liquid.
• The two ends of the tube are connected to the points whose difference is to be measured.
• It is used for measuring the difference of pressure between two points in the flow section to which it is connected.
• It is used in two conditions
  • In underground pipeline
  • When the specific gravity of manometric fluid is less than 1

Concept:
Pressure intensity at any point in a fluid, P = ρ×g×h
Where,
ρ = mass density of fluid which is assumed to be constant along with the depth, g = acceleration due to gravity, h = height of fluid measured from the free surface.
1 litre = 10^-3 m³
1 bar = 10⁵ pascal
Calculation:
Given:
S = 13.6 kg/liter, ρ = 13.6 × 10³ kg/m³, h = 12 cm = 0.12 m
P = ρ×g×h = 13600 × 0.12 × 10 = 16320 pascal = 0.1632 bar

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.

Concept:
Differential Manometers:

• Differential manometers are devices used for measuring the difference of pressures between two points in a pipe or in two different pipes.
• A differential manometer consists of a U-tube, containing a heavy or light liquid, whose two ends are connected to the points, whose difference of pressure is to be measured.
• The most common types of differential manometers are

1. U-tube differential manometer
2. Inverted U-tube differential manometer

• The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured.

U-tube differential manometer

• It consists of a U-tube containing a heavy liquid. 
• The two ends of the tube are connected to the points whose difference is to be measured. 
• It is used for measuring the difference of pressure between two points in the flow section to which it is connected.

Differential inverted U-tube manometer: 

• It consists of an inverted U-tube containing a light liquid.
• The two ends of the tube are connected to the points whose difference is to be measured.
• It is used for measuring the difference of pressure between two points in the flow section to which it is connected.
• It is used in two conditions
  • In underground pipeline
  • When the specific gravity of manometric fluid is less than 1

Concept:
Hydrostatic law:
In a static fluid, the pressure depends on the vertical depth from the surface and it is independent of the shape and size of the container.

Calculation:
Given:

Specific gravity ∝ density
∴ 
= 0.5

• Manometers are devices in which columns of a suitable liquid are used to measure the difference in pressure between two points or between a certain point and the atmosphere.
• A manometer is needed for measuring large gauge pressures. It is basically the modified form of the piezometric tube.

• A common type of manometer is like a transparent "U-tube" as shown in Figure:
  

These are of two types:

1. Simple manometers
2. Differential manometers

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 atmosphere.

Concept:
Differential manometer:
Differential manometers are the devices used for measuring the differences of pressures between two points in a pipe or in two different pipes. 
Most common types of differential manometers are:
1) U-tube differential manometer
A differential manometer consists of a U-tube, containing heavy liquid, whose two ends are connected to the points, whose difference of pressure is to be measured.

h = Difference of mercury level in the U-tube
y = Distance of the centre of B, from the mercury level in the right limb
x = Distance of the centre of A, from the mercury level in the right limb
ρ₁ = Density of liquid at A
ρ₂ = Density of liquid at B
ρ_g = Density of heavy liquid or mercury
Hence the difference in the pressure between A and B, when A and B are at different level is given by,
P_A – P_B = h × g × (ρ_g – ρ₁) +ρ₂gY – ρ₁gX  
Hence the difference in the pressure between A and B, when A and B are at same level is given by,
P_A – P_B = g × h × (ρ_g – ρ₁)    
2) Inverted U-tube differential manometer
It consists of an inverted U-tube, containing light liquid. It is used for measuring difference of low pressures
Calculation:
Given,
Oil specific gravity = 0.9
Difference in mercury level = 15 cm = 0.15 m
ρ_hg = 13600 kg/m³ 
ρ_oil = 0.9 × 1000 = 900 kg/m³

P_A + [900 × g × (Y + 0.15)] = P_B + (900 × g × Y) + [0.15 × g × 13600]
P_A - P_B = (13600 × g × 0.15) - (900 × g × 0.15)
PA - PB = 18688 N/m²

Concept:
U tube manometers:

• A U-tube manometer is the simplest pressure measurement device.
• Its name comes from the U-shape formed when the two ends of a flexible tube full of liquid are raised to keep the liquid from coming out the ends.
• A simple U tube manometer connected to a pipe in which liquid is flowing with uniform speed will give Gauge pressure.

Gauge pressure:
Gauge pressure is the pressure relative to atmospheric pressure. Most of the pressure measuring devices are calibrated to read gauge pressure.

• Gauge pressure is positive for pressures above atmospheric pressure.
• Gauge pressure is negative for pressures below atmospheric pressure.
• Gauge pressure is zero at atmospheric pressure.

Atmospheric pressure:
Atmospheric pressure or barometric pressure is the pressure within the atmosphere of Earth. Atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point.
P_atm = 1.013 bar.
Absolute pressure:
Absolute pressure is the sum of gauge pressure and atmospheric pressure.
P_abs = P_gauge + P_atm .

Manometer:
It is the device used for measuring pressure at a point in a fluid by balancing the column of fluid with the same or another column of liquid. manometers can be classified as follow:
1. simple manometer:

• Piezometer.
• U tube manometer.
• Single column manometer.

2. Diffrential type mano meter:
A Differential type manometer is a type of manometer which is used to measure the pressure difference between two points in a pipe.
U - tube differential manometer:
case-1
The below figure shows a differential manometer whose two ends are connected with two different points A and B at the same and contain the same liquid.

Where,
h = Difference in mercury level in the U- tube.
h₁ = Distance of center at A from mercury level at the right limb.
S₁ = S₂ =Speciic gravity of liquid at two points A and B.
S = specific gravity of heavy liquid or mercury in a U tube.
h_A = Pressure head at A.
h_B = Pressure head at B.
Difference in pressure head 
h_A - h_B = h(S - S₁).
Case - 2:
The figure below shows a differential manometer whose two ends are connected with two different points A and B at different levels and containing different liquids.

Where,
h₁ = Distance of the center of A from the mercury level at the left limb.
h₂ = Distance of the center of B from the mercury level at the right limb.
S₁ = Specific gravity of liquid in pipe A.
S₂ = Specific gravity of liquid in pipe B.
The difference in pressure head at pint A and B.
h_A - h_B = h(S - S₁) + h₂S₂ - h₁S₁.
Calculation:
Given:
S₁ = 1.0
S = 13.6 (Specific gravity of mercury).
h = 600 mm.
Pressure difference = 600 × ( 13.6 - 1.0 ).
Pressure difference = 7560 mm = 7.56 m.
The correct answer is 7.56 m .