A pipe of varying area of cross-section is held such that its axis is horizontal. At two cross sections A and B, its radii are 8 cm and 4 cm. If velocity of water at A through the pipe is 16 cm `s^(-1)` and pressure at A is `10^( 6)` dyne/`cm^(2)` , find the pressure at cross-section B.

Explanation

To find the pressure at cross-section B of a pipe with varying cross-section, we can apply the principles of fluid dynamics, specifically the continuity equation and Bernoulli's theorem. Here’s a step-by-step solution:

### Step 1: Determine the Areas of Cross Sections A and B
Given the radii:
- Radius at A, \( r_A = 8 \, \text{cm} \)
- Radius at B, \( r_B = 4 \, \text{cm} \)

The area of a circle is given by the formula:
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