Concepts Of Physics MCQ Edition [Volume 1]PhysicsFluid Mechanics
Water flows in streamline motion through a tube having a horizontal axis. Consider two points, A and B , inside the tube at an identical horizontal level.
Options
- AThe pressures might be equal even when the tube possesses a nonuniform cross section
- BThe pressures are equal provided the tube has a uniform cross section
- CThe pressures at these points are never equal
- DThe pressures at A and B remain equal for any shape of the tube
Correct answer
B. The pressures are equal provided the tube has a uniform cross section
Step-by-step solution
According to Bernoulli's theorem for a horizontal flow of an ideal fluid: P + 1 2 v^2 = constant From the equation of continuity: A v = constant If the tube has a uniform cross-section, the area A is constant, which means the velocity v is constant throughout the tube. Therefore, the pressure P is equal at all points. This makes the second option correct. If the tube has a non-uniform cross-section, the velocity v will vary. However, if the cross-sectional areas at points A and B are equal ( A_A = A_B ), the veloci