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Venturi meter is a device used to measure the flow rate or discharge of fluid through a pipe. Venturimeter is an application of Bernoulli’s equation. Its basic principle is also depends on the Bernoulli equation i.e. velocity increases pressure decreases. The principle of venture meter is firstly developed by G.B. Venturi in 1797 but this principle comes into consideration with the help of C. Herschel in 1887. The principle is that when cross sectional area of the flow is reduced then a pressure difference is created between the different areas of flow which helps in measuring the difference in pressure. With the help of this pressure difference we can easily measure the discharge in flow.

**BERNOULLIS PRINCIPLE:**

Bernoullis principle states that with the increase in the velocity of the **fluid** its pressure decreases (or) decreases the fluid potential energy. Decreasing the fluid **pressure** in the areas where flow velocity is increased is called as **Bernoulli effect.**

## Venturimeter:

**Construction:**

Venturimeter is very simple in construction. It has following parts which are arranged in systematic order for proper operation these are inlet section called as converging cone, cylindrical throat and gradually diverging cone.

**1. Converging Section/Cone**:

It is the region where the cross section emerges into conical shape for the connectivity with the throat region. The converging region is attached to the inlet pipe(flow upstream) and its cross sectional area decreases from beginning to ending. One side it is attached with inlet and its other side are attached with the cylindrical throat. The angle of convergence is generally 20-22 degree and its length is 2.7(D-d). Here D is the diameter of inlet section and d is the diameter of throat. Due to the decrease in the cross sectional area the fluid accelerates and static pressure decreases. The maximum cone angle of the converging area is limited to avoid the venacontracta so the flow area will be minimum at the throat.

**2. Cylindrical Throat**:

It is middle part of the venturimeter and has lowest cross sectional area. The length is equal to diameter of throat. Generally the diameter of the throat is 1/4 to 3/4 of the diameter of the inlet pipe, but mostly it is ½ of the diameter of the pipe. diameter. The diameter of the throat remains same through out its length. The diameter of throat cannot reduce to its minimum suitable value because if cross sectional area decrease velocity increase and pressure decreases. This decrease in pressure goes below the vapour pressure which results in cavitation. To avoid cavitation a limited value of diameter is preferred.

**3. Diverging Section/Cone:**

Diverging section is the third part of this device. One side it is attached with outlet pipe. The diameter of this section is gradually increases. The diverging section has an angle 5 to 15 degree. The diverging angle is less than the converging angle due to this length of the diverging cone is larger than converging cone. The main reason of the small diverging angle to avoid flow separation from the walls and prevents the formation of eddies because flow separation and eddies formation will results in large amount of loss in energy. To avoid these losses proper angle of converging and diverging should be maintained.

**Reasons for the limitation of Divergent angle:**–

- To reduce adverse pressure gradient and reverse flow (unsteady flow)
- Prevent flow separation which causes frictional drag.
- To avoid head loss and cavitation effect

**Differential Manometer and Pressure Gauges: **

Differential manometer are used to measure the pressure in the flow through pipe and it is mounted between inlet pipe and throat. We can use different pressure gauges in place of differential manometer to measure the pressure and different sections. The pressure gauges are mounted at inlet and throat of the venturimeter. The diverging section is not used for measuring the discharge because at this section flow separation may occur. When fluid flow through the venture meter then pressure difference is created which measured by the differential manometer.

**Working of Venturimeter:**

Working of venturimeter is so simple. As already explained it works on the principle of Bernoulli’s equation, i.e. when velocity increases pressure decreases. Same principle is applicable here. The cross section area of throat is smaller than the cross-section area of the inlet pipe due to this the velocity of flow at throat section is greater than the inlet section, this happens according to continuity equation. The increase in the velocity of flow at the throat will results in decrease in the pressure at this section, due to this a pressure difference is developed between inlet and throat of the venturimeter. This pressure difference can be easily measured by using differential manometer between the inlet section and throat or by using two separate gauges at inlet and throat. By measuring the different pressure at the two different sections we can easily measure or calculate the flow rate through the pipe.

Its working can be describe into following points.

- The working of venturimeter is based on the Bernoulli’s principle. As the velocity increases pressure decreases.
- In the convergent region as the area and pressure decreases the velocity increases and has a favorable pressure gradient [ i.e., (dp/dx)<0 ] .
- In the throat region area and pressure are constant and the velocity is also constant and pressure gradient is zero [ i.e., (dp/dx) = 0 ] .
- The decrease in the pressure in between the inlet and throat is measured with the help of differential manometer.
- The value of height of mercury in the manometer which is obtained from difference of pressure heads is used to calculate discharge by using Bernoulli equation.
- As the cone angle of divergent region is limited to 5 – 7
^{0}reverse flow is eradicated. Here the pressure gradient is adverse[ i.e., (dp/dx>0) ] .

**Bernoulli’s equation :-**

Venturimeter is used to obtain the pressure difference only, the discharge rate is obtained by using Bernoulli’s equation.

Let the region before convergent region be section 1 and throat region be section 2 .

Let,

**d _{1}= diameter at inlet V_{1 }= velocity at inlet**

**P _{1}= pressure at inlet A_{1} = Area at inlet**

Similarly,

**d _{2} = diameter at throat V_{2} = velocity at throat**

**P _{2} = pressure at throat A_{2} = Area at throat**

Applying Bernoulli’s equation at sections 1 &2

**(P _{1}/ρg)+( V_{1} ^{2}/2g)+Z_{1} = (P_{2}/ρg)+( V_{2} ^{2}/2g)+Z_{2}**

As the pipe is horizontal, so **Z _{1} = Z_{2}**

**(P _{1}-P_{2})/ρg = (V_{2} ^{2} – V_{1} ^{2}) / 2g**

The difference of pressure heads measured is called “h” .

Since **h = (P _{1}-P_{2})/ρg**

**h = (V _{2} ^{2} – V_{1} ^{2}) / 2g**

But by applying continuity equation at 1 & 2 sections

We have

**A _{1}V_{1} = A_{2}V_{2}**

**V _{1} = A_{2}V_{2} / A_{1}**

**h = (V _{2} ^{2}/2g) [ (A_{1}^{2} – A_{2}^{2}) / A_{1}^{2}]**

But for discharge

**Q = A _{1}V_{1} = A_{2}h** , So

The above discharge expression is for ideal cases and is known as Theoretical discharge.

In real Actual discharge is less that Theoretical discharge.

Where C_{d} is the coefficient of venturimeter and it is always less than 1 (i.e., C_{d }< 1)

**Another way to find “h” by using differential U – Tube Manometer :-**

Depending upon the flowing fluid and the manometer liquid the expression for “h” differs and given by differential U-Tube manometer.

**Case – I :-** If the liquid in the manometer is heavier than the flowing fluid in the pipe.

**h = x [(S _{h} / S_{0}) – 1]**

**Case – II :- **If the liquid in the manometer is heavier than the flowing fluid in the pipe.

**h = x [1- (S _{L}/ S_{0})]**

Here **S _{0}** = specific gravity of flowing fluid

**S _{L}** = specific gravity of lighter liquid

**S _{h}** = specific gravity of heavier liquid

**X** = difference of liquid columns in U – Tube

**NOTE :-**

- The section 1 is the region at inlet( before convergent part )
- P
_{1}is the pressure of fluid in the inlet pipe before entering the converging region.

**Application of Venturimeter: **

1. As discussed above venturimeter is used to measure the discharge in flow through pipes.

2. In medical applications it is used to measure the rate of flow in the arteries.

3. It has some other industrial applications like in gas, liquids, oil where pressure loss should be avoided.

4. It also measures the discharge of fluid which has some slurry or dirt particles because of its smooth design.

**Advantages:**

- The main advantage of venturimeter is it has very less losses and high accuracy.
- It has high coefficient of discharge.
- Easy to operate.
- It can be installed in any direction between pipe flow i.e. horizontal, vertical and inclined.
- Venturimeter has high accuracy as compare to other flow measuring devices like orifice meter, pitot tube and nozzles.

**Disadvantages:**

Venturimeter has some disadvantages also like, it has high initial cost because its calculation is very complicated.

- The major drawback of the venture meter is we cannot use it for small diameter size pipe.
- It is difficult in maintenance and inspections.
- Initial cost is high.

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