Flow Measurement MCQ Quiz in मल्याळम - Objective Question with Answer for Flow Measurement - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Explanation:

A Venturi meter is a device used for measuring the rate of flow of a fluid flowing through a pipe.

The working of the venturi meter is based on the principle of Bernoulli’s equation.

The Venturi meter is divided into 3 parts:

convergent cone, divergent cone, and throat.

Convergent cone: It is the region where the cross-section emerges into a conical shape for the connectivity with the throat region. The converging region is attached to the inlet pipe and its cross-sectional area decreases from beginning to end.

One side is attached with the inlet and its other side is attached to the cylindrical throat.

The angle of convergence is generally 20-22 degrees and its length is 2.7(D-d). Here D is the diameter of the inlet section and d is the diameter of the throat.

Additional information:

Throat: It is the middle part of the venturi meter and has the lowest cross-sectional area. The length is equal to the diameter of the throat. Generally, the diameter of the throat is 1/4 to 3/4 of the diameter of the inlet pipe.

The diameter of the throat remains the same throughout its length. The diameter of the throat cannot reduce to its minimum suitable value because if the cross-sectional area decreases velocity increases and pressure decreases.

Diverging cone: Diverging section is the third part of this device. One side it is attached to the outlet pipe. The diameter of this section is gradually increasing.

Explanation:

Explanation:

Pitot tube:

• It is based on the principle of conversion of kinetic head into pressure head.
• It measures the dynamic pressure of a moving fluid
• The point at which velocity reduces to zero is called the Stagnation point.
• Velocity head is indicated by the difference in liquid level between the pitot tube and the piezometer
• The pitot tube measures the total head therefore known as the total head tube.

Stagnation head = static head + dynamic head

Additional Information

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.

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.

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:

Concept:

\(Q = \frac{{{C_d}{A_1}{A_2}\sqrt {2gH} }}{{\sqrt {A_1^2 - A_2^2} }}\)

\(\therefore Q \propto \sqrt H \)

\(\therefore \;Q = C\sqrt H \)  ......(1)            

\(dQ = C\frac{dH}{{2\sqrt H }}\) ......(2)    

Taking ratio of equation (2) and (1).

\(\frac{{dQ}}{Q} = \frac{{C\left( {\frac{dH}{{2\sqrt H }}} \right)}}{{C\sqrt H }} = \frac{1}{2}\frac{{dH}}{H}\)

\(\therefore \;\frac{{dQ}}{Q} = \frac{1}{2}\frac{{dH}}{{H}}\)

Calculation:

Given:

\(\frac{{dH}}{H} = 5\% \)

\(\frac{{dQ}}{Q} = \frac{1}{2}\frac{{dH}}{{H}}\)

\(\therefore \frac{{dQ}}{Q} = \frac{1}{2} \times 5\% = 2.5\%\)

Concept:

Pitot Tube:

• It is used to measure the velocity of a fluid moving through a pipe by taking advantage of the fact that the velocity at the stagnation point is zero.
• As a result, kinetic energy gets converted into potential energy, resulting in a change in manometer height.

Applying Bernoulli's theorem:

\(\frac{P_1}{γ_{w}} + \frac{V_1^2}{2g}+Z_1=\frac{P_2}{γ_{w}} + \frac{V_2^2}{2g}+Z_2\)

⇒ \(\frac{V_1^2}{2g} = \frac{P_2-P_1}{γ_w}\)         ...(1)

∴ The velocity of the flow,

V1 = V = \(\sqrt{\frac{2(P_2-P_1)}{\rho}}\) 

Here,

V1 - Velocity of fluid in pipe = V

V2 = 0, Stagnation point velocity

P1 - Static pressure

P2 - Pressure at the stagnation point

Z1 = Z2, Elevation head for both the points

γw - The unit weight of water

Explanation:

From the above equation (1)

It is clear that the differential manometer is measuring the difference between two pressure heads (i.e. Stagnation pressure head and static pressure head) which is equal to the dynamic pressure head.

We know,

Pitot tube measures velocity at a stagnation pressure point.

Also, Stagnation pressure head = Static pressure head + Velocity head

⇒ Velocity head (or Dynamic head) = Stagnation pressure head - Static pressure head

This pressure head difference is measured by the manometer.

Hence, the Dynamic pressure head is correct.

Important Points

1. Static pressure:  It is the actual thermodynamic pressure of the fluid and does not incorporate any dynamic effects i.e. P.

2. Dynamic pressure: It represents the pressure rise when the fluid in motion is brought to a stop isentropically i.e. \(\frac{ρ V^2}{2}\).

3. Hydrostatic pressure: Pressure at a point in the fluid due to its weight and it depends on the reference selected i.e. ρgh.

4. Total pressure: Sum of all the pressures i.e. P + \(\frac{ρ V^2}{2}\) + ρgh.

5. Stagnation pressure: Sum of static pressure and dynamic pressure i.e. P + \(\frac{ρ V^2}{2}\).