Question

Explain with neat labeled diagram measurement of flow using a venturimeter.

Answer 1

A Venturi meter is a device used to measure the flow rate of a fluid through a pipe. It operates based on the principle of fluid dynamics, specifically the Bernoulli principle, which relates the speed of the fluid to its pressure.

### Basic Principle

The Venturi meter works on the principle that the velocity of a fluid increases as it passes through a constricted section of a pipe, which leads to a decrease in pressure. By measuring the pressure difference between the wide and narrow sections of the pipe, the flow rate can be determined.

### Diagram and Explanation

Here’s a simplified and labeled diagram of a Venturi meter:

```
+---------------------+    +-------------------+    +---------------------+
|                     |    |                   |    |                     |
|  Inlet Section      |    |  Constricted      |    |  Outlet Section     |
|    (Wide Pipe)      |----|    Section        |----|   (Wide Pipe)       |
|                     |    |  (Narrow Pipe)    |    |                     |
+---------------------+    +-------------------+    +---------------------+
                        |                         |
                        |                         |
                        |                         |
                        |                         |
                 +--------------+        +----------------+
                 |   Pressure   |        |   Pressure     |
                 |   Tap (P1)   |        |   Tap (P2)     |
                 +--------------+        +----------------+
```

### Components

1. **Inlet Section (Wide Pipe):** This is where the fluid enters the Venturi meter. The cross-sectional area is larger here, and the flow speed is relatively lower.
   
2. **Constricted Section (Narrow Pipe):** The fluid flows through a narrower section of the pipe. According to the continuity equation, the velocity of the fluid increases in this region, and the pressure decreases.

3. **Outlet Section (Wide Pipe):** After passing through the constricted section, the fluid enters another wide section where the velocity decreases, and the pressure increases back towards the original pressure.

4. **Pressure Taps (P1 and P2):** These are small openings used to measure the pressure at different sections of the pipe. Pressure tap P1 is located in the wide section before the constriction, and P2 is located in the constricted section.

### Working

1. **Flow Through the Meter:** As fluid flows through the Venturi meter, it first enters the wider inlet section. The velocity of the fluid is lower here, resulting in higher pressure.

2. **Constricted Section:** When the fluid reaches the constricted section, its velocity increases due to the reduced cross-sectional area. According to Bernoulli's equation, the pressure in this section drops.

3. **Pressure Measurement:** The pressure difference between the inlet section (P1) and the constricted section (P2) is measured using pressure taps. This pressure difference is related to the flow rate.

4. **Flow Rate Calculation:** The flow rate (Q) can be determined using the following formula derived from Bernoulli’s equation and the continuity equation:

   \[
   Q = A_1 \cdot A_2 \cdot \sqrt{\frac{2 \cdot (P1 - P2)}{\rho \cdot ( \frac{1}{A_2^2} - \frac{1}{A_1^2} )}}
   \]

   Where:
   - \( A_1 \) and \( A_2 \) are the cross-sectional areas of the inlet and constricted sections, respectively.
   - \( P1 \) and \( P2 \) are the pressures in the inlet and constricted sections, respectively.
   - \( \rho \) is the density of the fluid.

### Summary

The Venturi meter is a practical and widely used device for measuring flow rates in various applications, including water supply systems and industrial processes. Its operation is based on fundamental principles of fluid dynamics, specifically the relationship between pressure and velocity changes in different cross-sectional areas of the pipe.

Answer 2

### **Measurement of Flow Using a Venturimeter**

A **Venturimeter** is a device used to measure the flow rate or discharge of fluid in a pipe. It works based on the principle of Bernoulli's equation, which relates the pressure, velocity, and elevation in a flowing fluid.

### **Components of a Venturimeter**
1. **Inlet Section (Converging Cone):**
   - The first part of the Venturimeter is the converging section. Here, the cross-sectional area of the pipe decreases gradually, causing the fluid velocity to increase and pressure to decrease.

2. **Throat:**
   - The throat is the narrowest part of the Venturimeter. The velocity of the fluid is at its maximum, and the pressure is at its minimum.

3. **Outlet Section (Diverging Cone):**
   - After the throat, the fluid enters the diverging section where the cross-sectional area increases, causing the velocity to decrease and the pressure to increase again.

4. **Manometer:**
   - A differential manometer is attached at two points: one at the inlet section and one at the throat. The manometer measures the difference in pressure between these two points.

### **Working Principle**
- When fluid flows through the Venturimeter, it enters the converging section where its velocity increases, causing a drop in pressure according to Bernoulli's principle.
- The fluid then passes through the throat, where the velocity is highest and the pressure is lowest.
- In the diverging section, the velocity decreases, and the pressure increases.

By measuring the pressure difference between the inlet and the throat using the manometer, and knowing the dimensions of the Venturimeter, the flow rate of the fluid can be calculated using the following formula derived from Bernoulli's equation:

\[ Q = A_1 A_2 \sqrt{\frac{2 \Delta P}{\rho \left(A_1^2 - A_2^2\right)}} \]

Where:
- \( Q \) = Discharge or flow rate (m³/s)
- \( A_1 \) = Area of the inlet section (m²)
- \( A_2 \) = Area of the throat section (m²)
- \( \Delta P \) = Pressure difference between the inlet and throat (Pa)
- \( \rho \) = Density of the fluid (kg/m³)

### **Neat Labeled Diagram**

Here's a description of how the diagram would look:

1. **A horizontal pipe** with an inlet (left) connected to the fluid source.
2. **Converging section** leading to a **throat** (narrowest point in the middle).
3. **Diverging section** after the throat (right side) leading to the outlet.
4. **Two pressure tapping points**: One on the inlet section before the converging cone and another at the throat.
5. **Manometer** connected to the two tapping points, showing the pressure difference.

Would you like me to generate a diagram based on this description?