Pressure Measurement MCQ Quiz - Objective Question with Answer for Pressure Measurement - Download Free PDF

Concept: 

The relation between pressure and height of liquid column is: 

Calculation:

Given data: P = ; 

Explanation:

Manometer:

• Purpose: Measures the pressure at a point in a fluid using the height difference in a column of liquid (usually mercury or water).

• Types: Common types include U-tube, inclined, and differential manometers for measuring gauge and differential pressures.

• Working Principle: Based on hydrostatic pressure, i.e., the pressure exerted by a static fluid column.

• Applications: Used in laboratories, pipelines, gas systems, and HVAC systems to measure static pressures accurately.

 Additional InformationNozzle Meter

• Purpose: Used to measure the rate of flow (discharge) of fluid in a pipe using the Bernoulli principle and continuity equation.

• Construction: Consists of a converging nozzle installed in a pipeline and pressure taps at upstream and throat sections.

• Operation: Flow rate is calculated from the pressure difference between the two sections using a discharge coefficient.

• Comparison: Similar to venturimeter and orifice meter but is more compact and causes less pressure loss than an orifice meter.

Pitot Tube

• Purpose: Designed to measure the velocity of fluid flow, especially in open channels, ducts, or air streams.

• Working Principle: Measures the difference between static and stagnation pressure to determine velocity using Bernoulli’s equation.

• Structure: Consists of a tube pointing into the flow to capture stagnation pressure and holes on the side for static pressure.

• Applications: Widely used in aerodynamics, hydraulics, HVAC systems, and aircraft for airspeed measurement.

Hydrometer

• Purpose: Measures the specific gravity or density of a liquid by floating at a certain level based on buoyant force.

• Working Principle: Based on Archimedes’ principle, which states that a body immersed in fluid is buoyed up by a force equal to the weight of the displaced fluid.

• Scale Readings: The scale on the stem gives direct reading of specific gravity, which can relate to concentration or purity.

• Applications: Commonly used in battery maintenance, breweries, petroleum industry, and chemical labs to assess fluid quality.

Explanation:

Vacuum Pressure

• Vacuum pressure is an important concept in the field of fluid mechanics and engineering. It refers to the pressure below the atmospheric pressure in a system. In a vacuum, the pressure is reduced to a level lower than the atmospheric pressure, which is considered as the reference point. Vacuum pressure is measured as the difference between the atmospheric pressure and the absolute pressure within the system. It is commonly expressed in units such as pascals (Pa), millimeters of mercury (mmHg), or inches of mercury (inHg).
• Vacuum pressure can be created in a system by removing air or other gases using mechanical pumps or other methods. This is done to achieve various objectives, such as improving thermal insulation, enhancing the efficiency of certain processes, or creating a controlled environment for scientific experiments. Vacuum pressure is widely used in numerous industrial and scientific applications, including vacuum packaging, vacuum distillation, and vacuum chambers for testing materials and equipment.

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Explanation:

Gauge Pressure and Its Relation to Atmospheric Pressure

Definition: Gauge pressure is the pressure measured relative to the surrounding atmospheric pressure. It is commonly used in engineering and industrial applications to measure the pressure of fluids (liquids or gases) within a system. The concept of gauge pressure is essential because it excludes the atmospheric pressure, which simplifies the measurement process in most practical scenarios.

Working Principle:

To understand the relationship between gauge pressure and atmospheric pressure, it is necessary to understand the following terms:

• Absolute Pressure: The total pressure measured relative to a perfect vacuum. It is the sum of the atmospheric pressure and the gauge pressure.
• Atmospheric Pressure: The pressure exerted by the Earth's atmosphere at a given location and altitude. At sea level, atmospheric pressure is approximately 101.325 kPa or 1 atmosphere.
• Gauge Pressure: The pressure measured relative to the atmospheric pressure. Gauge pressure can be positive (when the system pressure is above atmospheric pressure) or negative (when the system pressure is below atmospheric pressure, also called vacuum pressure).

The relationship between these pressures is given by the following equation:

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

Or equivalently:

Gauge Pressure = Absolute Pressure - Atmospheric Pressure

This equation highlights that gauge pressure is the difference between the absolute pressure within a system and the atmospheric pressure. This relationship is crucial for understanding how gauge pressure behaves in different environments and under varying atmospheric conditions.

Correct Option Analysis:

The correct option is:

Option 3: Gauge pressure is the difference between absolute pressure and atmospheric pressure.

This option accurately describes the relationship between gauge pressure, absolute pressure, and atmospheric pressure. As explained above, gauge pressure is calculated by subtracting atmospheric pressure from the absolute pressure within a system. This definition aligns with the standard practices in pressure measurement and is universally accepted in engineering and scientific contexts.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Gauge pressure is independent of atmospheric pressure.

This statement is incorrect because gauge pressure is explicitly defined relative to atmospheric pressure. If atmospheric pressure changes (e.g., at higher altitudes or under different weather conditions), the gauge pressure reading for the same absolute pressure will also change. Therefore, gauge pressure is not independent of atmospheric pressure.

Option 2: Gauge pressure equals atmospheric pressure minus absolute pressure.

This option is incorrect because it reverses the actual relationship between gauge pressure, absolute pressure, and atmospheric pressure. As stated earlier, the correct formula is:

Gauge Pressure = Absolute Pressure - Atmospheric Pressure

Switching the terms, as suggested in this option, would lead to incorrect calculations and misunderstandings in practical applications.

Option 4: Gauge pressure is the sum of absolute and atmospheric pressure.

This option is incorrect because it misrepresents the relationship between the pressures. The sum of absolute pressure and atmospheric pressure would result in a value that has no physical meaning in the context of pressure measurement. Instead, the correct relationship is:

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

Gauge pressure is not the sum of absolute and atmospheric pressure.

Conclusion:

Understanding the relationship between absolute pressure, atmospheric pressure, and gauge pressure is fundamental to pressure measurement in engineering and scientific applications. Gauge pressure is the difference between absolute pressure and atmospheric pressure, making it a practical and widely used parameter for measuring the pressure of fluids within a system. The correct option, Option 3, accurately describes this relationship, while the other options misrepresent the fundamental concepts involved in pressure measurement.

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Concept:

Hydrostatic Pressure, P = ρgh

Where, ρ = Density, g = Acceleration due to gravity, h = Manometric head

Calculation:

Given:

h = 20 m, g = 9.81 m/s2, ρ = 1000 kg/m3 

∴ P = 1000 × 9.8 × 20 = 196000 = 196 kPa

The correct answer is Pascal's law.

• The Pascal's law states that in a fluid which is at rest in a container, the pressure applied to one part of the fluid is uniformly transmitted to all the parts of the fluid.

Key Points

• A hydraulic lift employs this principle to lift heavy objects.
• When pressure is applied to a fluid through one piston, it results in an equivalent pressure on another piston in the system which is then able to lift objects.
• With the increase in the area of the second piston, the force exerted by it also increases thus enabling lifting of heavier objects.

Additional Information

• Hooke's law states that force needed to extend or compress a spring by some distance is directly proportional to that distance.
• Newton's first law of motion - A body at rest remains at rest, or if in motion, remains in motion at constant velocity unless acted on by a net external force. 
• Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

Explanation:

The total energy of a flowing fluid can be represented in terms of head, which is given by

The sum of the pressure head and hydrostatic pressure head is called the piezometric head. It is given by 

Piezometric head = 

where = pressure energy per unit weight or pressure head

= kinetic energy per unit weight or kinetic energy head

z = potential energy per unit weight or elevation head

The pressure at any point in a static fluid is obtained by Hydro-static law which is given by -

∴ P = -ρgz

∴ P = ρgh

where P = pressure above atmospheric pressure and h = height of the point from the free surface.

At point A, pressure head =  = hA  and datum head = zA

At point B, pressure head =  = hB  and datum head = zB

Piezometric head at point A =  = hA + zA = H

Piezometric head at point B =  = hB + z₀ = H

∴ piezometric head remains constant at all points in the liquid.

Explanation:

A manometer is a device that measures pressure by balancing a column of liquid against a column of gas or another liquid. The liquid used in a manometer should have the following characteristics:

• The liquid should stick on the walls: The liquid used in a manometer should stick to the walls of the tube to prevent it from flowing back and forth due to vibration or turbulence.
• Low surface tension: The liquid used in a manometer should have low surface tension to ensure that the meniscus does not significantly affect the pressure reading.
• It should be immiscible: The liquid used in a manometer should be immiscible with the gas or liquid being measured, to prevent the two fluids from mixing and affecting the accuracy of the pressure measurement.
•  High viscosity is NOT a desirable characteristic for a manometer liquid. A highly viscous liquid will not respond quickly to changes in pressure, leading to slow and inaccurate readings. Thus, manometer liquids are typically chosen to have relatively low viscosity.

Explanation:

From hydrostatic law:

Rate of increase of pressure in a vertical direction equal to the weight density of the fluid at that point.

    ....eq (1)

For a compressible fluid, density (ρ) changes with the change of pressure and temperature. Thus, eq (1) cannot be integrated directly.

∵ Air is an ideal gas so,

ρ = p/RT (∵ PV = mRT)

∴ p = e^-gh/RT i.e. the atmospheric pressure varies exponentially with height.

Explanation:-

Manometer - 

A manometer is an instrument that uses a column of liquid to measure pressure, although the term is currently often used to mean any pressure instrument.

Two types of manometer, such as

1. Simple 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 the other end remains open to the atmosphere. Common types of simple manometers are:

• Piezometer
• U tube manometer
• Single Column manometer

2. Differential manometer

Differential Manometers are devices used for measuring the difference of pressure between two points in a pipe or in two different pipes. A differential manometer consists of a U-tube, containing a heavy liquid, whose two ends are connected to the points, which difference in pressure is to be measured.

The most common types of differential manometers are:

• U-tube differential manometer.
• Inverted U-tube differential manometer

3. Inclined U-tube manometer - 

If the pressure to be measured is very small. It is more accurate than a U-tube manometer.

Then tilting the arm provides a convenient way of obtaining a larger (more easily read) movement of the manometer.

The pressure difference is still given by the height change of the manometric fluid(z₂).

The sensitivity to pressure change can be increased further by a greater inclination of the manometer arm.

An alternative solution to increase sensitivity is to reduce the density of the manometric fluid.

Concept:

We know that; P = ρgh

In terms of specific gravity, P = h × G

Notice that all the options are given in terms of water column hence we will calculate on the basis of properties of water.

When Pressure is equivalent for two different liquids,

hHg  × SHg = hwater × Swater

Calculation:

Given:

S_Hg = 13.6

hHg  = 70 cm = 0.7 m

S_water= 1

hHg  × SHg = hwater × Swater

hwater = 13.6 × 0.7 = 9.52

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 ρ_oil.

ρ_oil × g × (d + l) = ρ_water × g × l

ρ_oil × (20 + 80) = 1000 × 80

ρ_oil = 800 kg/m3

Hence the required density of oil is 800 kg/m3.

Concept:

Mathematically, it can be represented as:

Absolute Pressure = Atmospheric pressure + Gauge Pressure.

Pabs = Pgauge + Patm

Calculation:

Given:

h = 5 m

P_atm = 0.75 m of mercury = ρ_Hg × g × 0.75 = 13600 × 9.81 × 0.75 = 100062 Pa

P_gauge = ρ_water × g × h

P_gauge = 1000 × 9.81 × 5 = 49050 Pa

P_abs = P_gauge + P_atm

P_abs = 49050 + 100062

P_abs = 149112 Pa = 149112 N/m² = 0.149 N/mm² ≃ 0.15 N/mm²

Concept:

Pabsolute = Patmospheric + Pgauge

The pressure at any point in a static fluid is obtained by Hydro-static law which is given by-

∴ P = -ρgz

P increases when we go down (z negative) and decreases when we go up (z positive).

where P = pressure above atmospheric pressure and h = height of the point from the free surface.

The difference in barometric (Atmospheric) pressure at sea level and that on the mountain is due to the elevation difference i.e. a pressure equivalent to the extra height of air column equal to the elevation of the mountain acting at the sea level as compared to on the mountain.

P_s = P_h + (ρ_a × g × h)

P_s = Pressure at the sea level, P_h = Pressure at the mountain top, ρ_a = Density of air, h = Height of mountain

Calculation:

Given:

P_s = 760 mm of Mercury, P_h = 724 mm of Mercury, ρ_a = 1.2 Kg/m³

∴ Ps = Ph + (ρa × g × h)

⇒ (ρa × g × h) = Ps - Ph

So,

(ρa × g × h) = (760 - 724) × 10^-3 × g × 13600

⇒ h = = 408 m

So, Height of the mountain is 410 meters.

Explanation:

Hydrostatic law:

The pressure at any point in a static fluid is obtained by Hydro-static law which is given by -

∴ P = -ρgz

∴ P = ρgh

where P = pressure above atmospheric pressure and h = height of the point from the free surface.

Specific Weight is the weight of a substance per unit volume.

Specific weight, w = 

where, m = mass, V = Volume

∴ the correct answer is specific weight.