Question

A fluid is forced through a pipe of changing cross section as shown. In which section would the pressure of the fluid be a minimum?

Answer 1

straight

Step-by-step explanation:

because it is good in that direction

Answer 2

The pressure is minimum in section III due to the largest cross-sectional area, following the principle of continuity and Bernoulli's equation. As area increases, velocity decreases, leading to higher pressure, making section III the optimal choice.

This is based on the principle of continuity, which states that the mass flow rate of a fluid is constant in a pipe, regardless of the cross-sectional area. Mathematically, this means that the product of the cross-sectional area and the fluid velocity is constant:
`\(A_1v_1 = A_2v_2\)`. Therefore, when the cross-sectional area increases, the fluid velocity decreases, and vice versa.

According to Bernoulli's equation, the pressure of a fluid is inversely proportional to its velocity, assuming the fluid is incompressible and the height is constant:
`\(P_1 + (1)/(2)\rho v_1^2 = P_2 + (1)/(2)\rho v_2^2\)`. Therefore, when the fluid velocity decreases, the pressure increases, and vice versa.

Hence, the pressure of the fluid is a minimum in section III, where the cross-sectional area is the largest and the fluid velocity is the smallest.