Concepts Of Physics MCQ Edition [Volume 1]
- Exam
- Concepts Of Physics MCQ Edition [Volume 1]
- Subject
- Physics
- Chapter
- Fluid Mechanics
Concepts Of Physics MCQ Edition [Volume 1] · Physics · Fluid Mechanics
Water flows in streamline motion through a tube having a horizontal...
Water flows in streamline motion through a tube having a horizontal axis. Consider two points, and , 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 and 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:
From the equation of continuity:
If the tube has a uniform cross-section, the area is constant, which means the velocity is constant throughout the tube. Therefore, the pressure is equal at all points. This makes the second option correct.
If the tube has a non-uniform cross-section, the velocity will vary. However, if the cross-sectional areas at points and are equal (), the velocities at these two points will be equal (). In this case, the pressures at and will be equal. This makes the first option correct.
From the equation of continuity:
If the tube has a uniform cross-section, the area is constant, which means the velocity is constant throughout the tube. Therefore, the pressure is equal at all points. This makes the second option correct.
If the tube has a non-uniform cross-section, the velocity will vary. However, if the cross-sectional areas at points and are equal (), the velocities at these two points will be equal (). In this case, the pressures at and will be equal. This makes the first option correct.