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Water flows steadily through a horizonta...

Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is `p` at a point where the velocity of flow is `v`, at another point (pressure `p'`), where the velocity of flow in `etav` : The following statements are given below

A

`(p')/(p) lt 1`, when `eta lt 1`

B

`(p')/(p) lt 1`, when `eta gt 1`

C

`(p')/(p) gt 1`, when `eta lt 1`

D

`(p')/(p) gt 1`, when `eta gt 1`

Text Solution

AI Generated Solution

To solve the problem, we will apply Bernoulli's equation for fluid flow in a horizontal pipe with variable cross-section. The key points to consider are the relationships between pressure and velocity at two points in the pipe. ### Step-by-Step Solution: 1. **Understanding Bernoulli's Equation**: For a horizontal flow, Bernoulli's equation states that the sum of pressure energy and kinetic energy per unit volume remains constant. Mathematically, it can be expressed as: \[ P + \frac{1}{2} \rho v^2 = P' + \frac{1}{2} \rho (eta \cdot v)^2 ...
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