Orificemeter MCQ Quiz - Objective Question with Answer for Orificemeter - Download Free PDF

Classification of Orifices

Orifices can be classified based on various criteria, including the shape of the orifice, the edge type, and the nature of discharge. In the given question, the classification is based on the nature of discharge, which focuses on whether the flow is free or submerged.

Analyzing the Given Options

1. "Drowned orifice." (Correct Answer)

   • A drowned orifice, also known as a submerged orifice, occurs when the downstream water level is higher than the top of the orifice, causing the flow to be submerged. This classification is based on the nature of discharge.

   • In this case, the entire orifice is under water, and the discharge characteristics are influenced by the downstream water level.

2. "Sharp-edged orifice." (Incorrect Answer)

   • A sharp-edged orifice is classified based on the edge type, not the nature of discharge. It has a thin edge that creates a clear, well-defined jet.

3. "Circular orifice." (Incorrect Answer)

   • A circular orifice is classified based on its shape, not the nature of discharge. It refers to an orifice with a circular opening.

4. "Bell-mouthed orifice." (Incorrect Answer)

   • A bell-mouthed orifice is classified based on its shape, specifically its flared or bell-shaped opening, which reduces the contraction of the jet.

Concept:

The actual discharge through an orifice is generally lower than the theoretical discharge due to energy losses such as:

• Friction losses within the orifice.
• Flow contraction (vena contracta effect) reducing the effective flow area.
• Viscous effects in real fluids.

Theoretical discharge is given by Torricelli’s theorem:

\( Q_{\text{theoretical}} = A \sqrt{2gh} \)

The actual discharge is calculated using the discharge coefficient \( C_d \):

\( Q_{\text{actual}} = C_d A \sqrt{2gh} \)

Since real flow experiences losses, the coefficient of discharge \( C_d \) is always less than 1.

Explanation:
Discharge Q through a venturimeter or an orificemeter is given by

\(\begin{array}{l} Q = {C_d}\frac{{{a_1}{a_2}}}{{\sqrt {a_1^2 - a_2^2} }}\sqrt {2gh} \\ \therefore h \propto \frac{1}{{C_d^2}}\\ \therefore \frac{{{h_v}}}{{{h_o}}} = {\left( {\frac{{{C_{d,o}}}}{{{C_{d,v}}}}} \right)^2} = {\left( {\frac{{0.61}}{{0.98}}} \right)^2} \end{array}\)

Explanation:

Correct Option Analysis:

The correct option is option 4: Blocked orifices.

An orifice is a small opening or hole, typically used to control the flow of fluids, including gases and liquids. The classification of orifices is based on the conditions under which they operate, and how they manage the flow of the fluid passing through them. The correct classification of orifices includes:

• Free Discharging Orifices: These orifices discharge fluid into the atmosphere or into a space where the pressure is relatively low, without any significant back pressure. The fluid exits the orifice freely.
• Drowned Orifices: These orifices are fully submerged in the fluid on both sides. The fluid flow through the orifice is influenced by the pressure differential across the orifice.
• Submerged Orifices: Similar to drowned orifices, submerged orifices are those where the exit is submerged in the fluid. The flow characteristics are determined by the difference in fluid levels and pressures on either side of the orifice.

Blocked orifices, on the other hand, are not a recognized classification of orifices. A blocked orifice would imply that there is no flow through the orifice, which defeats the purpose of having an orifice in the first place. Orifices are designed to allow controlled flow of fluid, and if an orifice is blocked, it no longer serves its functional purpose.

Therefore, option 4 is the correct answer as it does not fit within the recognized classifications of orifices.

Additional Information

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

Option 1: Free discharging orifices

Free discharging orifices are a valid classification of orifices. These orifices discharge fluid into the atmosphere or an environment with minimal back pressure. The fluid exits the orifice freely, and the flow characteristics are determined by the pressure and velocity of the fluid as it exits.

Option 2: Drowned orifices

Drowned orifices are another valid classification. These orifices are fully submerged in the fluid, meaning that both the entry and exit points of the fluid are within the fluid medium. The flow is influenced by the pressure difference across the orifice and the fluid characteristics.

Option 3: Submerged orifices

Submerged orifices are also a recognized classification. In this case, the exit of the orifice is submerged in the fluid. The flow is determined by the fluid levels and pressures on both sides of the orifice. These orifices are commonly used in applications where precise control of fluid flow is required under submerged conditions.

Conclusion:

Understanding the correct classifications of orifices is crucial for applications in fluid dynamics and engineering. Orifices are designed to control and regulate fluid flow, and their classifications are based on the operational conditions under which they function. Blocked orifices are not a recognized classification because they do not permit fluid flow, which is contrary to the purpose of an orifice. Therefore, option 4 is correctly identified as not being a classification of orifices.

Explanation:

As per given data:

• Tank dimensions: 2 m × 1.5 m

• Tank height: 6 m

• Orifice diameter: 100 mm = 0.1 m

• Initial water level: 5 m

• Final water level: 3.5 m

• Discharge coefficient (Cₓ): 0.6

• Acceleration due to gravity (g): 10 m/s²

Let at any instant depth of liquid in the tank is 'h' m and in time (dt), the depth falls by (-dh)

Q.dt = A₀(-dh) 

\(\Rightarrow\left(C_d \cdot\left(\frac{\pi d^2}{4}\right) \sqrt{2 g h}\right) d t=A_0(-d h)\)

\(t=\int d t=\frac{A_0}{C_d \cdot \frac{\pi d^2}{4} \sqrt{2 g}} \int_{H_1}^{H_2}\left(\frac{-d H}{\sqrt{h}}\right) \)

\(t=\frac{A_0}{C_d \cdot \frac{\pi d^2}{4} \sqrt{2 g}}\left[2\left(\sqrt{H_1}-\sqrt{H_2}\right)\right]\)

\(t=\left[\frac{2 \times 1.5 m^2}{0.6 \times \frac{\pi}{4}(0.1)^2 m^2 \sqrt{2 \times 10 \frac{m}{s^2}}} \times 2(\sqrt{5}-\sqrt{3.5}) \mathrm{m}^{1 / 2}\right] \mathrm{sec} \)

t = 103.985 sec

Explanation:

Coefficient of discharge is the ratio of actual discharge to the theoretical discharge.

\(\rm C_d=\frac{Actual \;discharg}{Theoretical\:discharge}\)

Coefficient of discharge for various devices are:

⇒ Venturimeter – 0.95 to 0.98

⇒ Orifice meter – 0.62 to 0.65

⇒ Nozzle  – 0.93 to 0.98

Concepts:

The coefficient of discharge (C_d) is the ratio of the actual discharge (Q_a) to theoretical discharge (Q_th) .

The actual discharge is the discharge obtained when all the looses through orifice or pipe flow are considered. While, theoretical discharge is the discharge obtained under ideal conditions i.e. no loss is considered.

The  theoretical discharge is given as:

Q_th = A × V_th

V_th is the theoretical velocity of flow

Calculations:

Given: V_th = 2 m/s; A = 0.4 m²

So, Q_th = 0.4 × 2 = 0.8 m³/s  or 800 l/s

∴ C_d = 400/800

C_d = 0.5

Other important Coefficients:

1. Coefficient of velocity is the ratio of actual velocity to theoretical velocity.

2. Coefficient of contraction is the ratio of cross-section area at vena-contracta to original cross- sectional area.

Explanation:

Coefficient of velocity:

It is defined as the ratio of the actual velocity of the jet at vena contracta V to the theoretical velocity V_th.

Experimentally it is determined by using the following relation

\({C_V} = \sqrt {\frac{{{x^2}}}{{4\;y\;h}}} \)

where x = Horizontal distance

y = vertical distance

h = constant head water

Generally, the value of Cv varies from 0.95 to .99 for different orifices depending upon their size, shape, head etc.

for sharp edged orifices the value of Cv is 0.98.

Concept:

Discharge through a circular orifice is given by;

\(Q = {C_d}a\sqrt {2gh} \)

Where, a = Area of orifice

h = Head above the surface

Calculation:

Given,

Discharge through the orifices are same

h₁ = 25 cm, h₂ = 1 m = 100 cm

∵ we know that, \(Q = {C_d}a\sqrt {2gh} \)

and, Q₁ = Q₂

⇒ \({C_d}{a_1}\sqrt {2g{h_1}} = {C_d}{a_2}\sqrt {2g{h_2}} \)

⇒ \(\frac{\pi }{4} \times d_1^2\sqrt {{h_1}} = \frac{\pi }{4} \times d_2^2\sqrt {{h_2}} \)

\(\frac{{d_1^2}}{{d_2^2}} = \sqrt {\frac{{{h_2}}}{{{h_1}}}} = \sqrt {\frac{{100}}{{25}}} = 2\)

\(\frac{{{d_1}}}{{{d_2}}} = \sqrt 2 \)

Explanation:

• As the fluid flows pressure drops along the direction of flow due to losses. Hence the more the losses along the flow the more will we be the pressure drop.
• Coefficient of discharge (C_d) is the measure of flow efficiency. It means higher the value of  Cd lesser will be the losses.
• Venturimeter is more efficient than the Orifice meter. Hence the coefficient of discharge is higher for Venturimeter than for Orifice meter.

Now,

\(Pressure\ drop\ (Δ P) ∝ \frac{1}{Coefficient\ of\ discharge\ (C_d)}\)

∵ (C_d)_venturimeter  > (C_d)_{orifice meter} 

∴ (ΔP)_venturimeter < (ΔP)_{orific meter}

Hence if Orific is replaced by a Venturimeter in a pipe then the pressure drop will decrease.

Additional Information

Venturimeter:

• A venturi meter is a device used for measuring the rate of flow of a fluid of a liquid flowing through a pipe
• The venturi meter always have a smaller convergent portion and larger divergent portion
• The size of the venturi meter is specified by its pipe diameter as well as throat diameter.

• This is done to ensures a rapid converging passage and a gradual diverging passage in the direction of flow to avoid the loss of energy due to the separation
• In the course of flow through the converging part, the velocity increases in the direction of flow according to the principle of continuity, while the pressure decreases according to Bernoulli’s theorem
• The velocity reaches its maximum value and pressure reaches its minimum value at the throat
• Subsequently, a decrease in the velocity and an increase in the pressure take place in course of flow through the divergent part
• The angle of convergence ≈ 20°, Angle of divergence = 6° - 7°. It should be not greater than 7° to avoid flow separation

Orifice meter:

• An orifice meter provides a simpler and cheaper arrangement for the measurement of flow through a pipe.
• An orifice meter is essentially a thin circular plate with a sharp-edged concentric circular hole in it.

Cd is defined as the ratio of the actual flow and the ideal flow and is always less than one. 

For orifice meter, the coefficient of discharge Cd depends on the shape of the nozzle, the ratio of pipe to nozzle diameter and the Reynolds number of the flow.

An orifice meter provides a simpler and cheaper arrangement for the measurement of flow through a pipe. An orifice meter is essentially a thin circular plate with a sharp-edged concentric circular hole in it.

Cd is defined as the ratio of the actual flow and the ideal flow and is always less than one. 

For the orifice meter, the coefficient of discharge C_d depends on the shape of the nozzle, the ratio of pipe to nozzle diameter and the Reynolds number of the flow.

Important Points

The coefficient of discharge is shows as the losses inflow. Since in laminar flow losses are less and in turbulent losses is more hence the value of the coefficient of discharge also varies with the type of flow. As we know Reynold number shows the type of flow occurring hence we can say that the coefficient of discharge also depends upon the Reynold number.

Explanation:

Orifice meter:

• An orifice meter is a cheap device for discharge measurement.
• The coefficient of discharge (Cd) is defined as the ratio of actual discharge to the ideal discharge.

 C_d =\(\frac{\text { Actual discharge }}{\text { Theoretical discharge }}\) 

• The value of Ca carries between 0.61 to 0.65.

Explanation:

Concept:

Coefficient of discharge (C_d) is defined as:

\(C_d=\frac{Q_{actual}}{Q_{theoretical}}\)

Theoretical discharge (Q_theoretical) can be calculated by:

Qtheoretical = Area of orifice × velocity of flow

Velocity of flow (V) can be calculated by:

\(V = \sqrt{2gh}\)

where h is head of fluid over the orifice

Calculation:

Given:

h = 5 m, Area = 0.1 m², C_d = 0.4

Velocity of flow is:

\(V = \sqrt{2gh}\)

\(V = \sqrt{2×10×5}=10~m/s\)

Theoretical discharge (Qtheoretical) is:

Qtheoretical = Area of orifice × velocity of flow

Qtheoretical = 0.1 × 10 = 1 m³/s

We know that,

\(C_d=\frac{Q_{actual}}{Q_{theoretical}}\)

Actual discharge is:

Q_actual = C_d × Q_theoretical 

Q_actual = 0.4 × 1 = 0.4 m³/s

Explanation:

Vena contracta:

• The section of least cross-section and hence of maximum contraction is called vena contracta.
• Since the area is minimum, the velocity is maximum at the vena contracta.
• It occurs about one half orifice diameter away from the downstream edge of the orifice.
• Formation of vena contracta is caused by the change in direction of motion of the liquid particles approaching the orifice.
• Beyond vena contracta, the streamline becomes parallel to each other.