A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement from the following

Options

A. The speed is high at the wider end and low at the narrow end
B. The speed is low at the wider end high at the narrow end
C. The speed is same at both ends in a streamline flow
D. The liquid flows with unifrom velocity in the tube

Answer

To solve the problem regarding the flow of liquid through a truncated cone-shaped tube, we can follow these steps:

### Step 1: Understand the Geometry of the Tube
The tube has a truncated cone shape, which means it has two ends with different diameters. Let’s denote:
- A1 = Cross-sectional area at the narrow end
- A2 = Cross-sectional area at the wider end

### Step 2: Apply the Continuity Equation
According to the principle of conservation of mass for incompressible fluids, the product of the cross-sectional area and the velocity of the fluid must remain constant along the tube. This is expressed mathematically as:
\[ A_1 V_1 = A_2 V_2 \]

Where:
- V1 = Velocity of the liquid at the narrow end (A1)
- V2 = Velocity of the liquid at the wider end (A2)

### Step 3: Rearrange the Continuity Equation
From the continuity equation, we can express the velocities in terms of the areas:
\[ V_1 = \frac{A_2}{A_1} V_2 \]

### Step 4: Analyze the Areas
Since the area A2 (wider end) is greater than A1 (narrow end), we can conclude that:
\[ A_2 > A_1 \]

### Step 5: Determine the Relationship Between Velocities
From the rearranged equation, since A2 is greater than A1, it follows that:
\[ V_1 > V_2 \]

This means that the velocity of the liquid is higher at the narrow end (A1) and lower at the wider end (A2).

### Conclusion
Thus, the correct statement is that the speed of the liquid is higher at the narrow end and lower at the wider end.