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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, AA and BB, inside the tube at an identical horizontal level.

Options

  1. AThe pressures might be equal even when the tube possesses a nonuniform cross section
  2. BThe pressures are equal provided the tube has a uniform cross section
  3. CThe pressures at these points are never equal
  4. DThe pressures at AA and BB 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+12ρv2=constantP + \dfrac{1}{2}\rho v^2 = \text{constant}

From the equation of continuity:

Av=constantA v = \text{constant}

If the tube has a uniform cross-section, the area AA is constant, which means the velocity vv is constant throughout the tube. Therefore, the pressure PP is equal at all points. This makes the second option correct.

If the tube has a non-uniform cross-section, the velocity vv will vary. However, if the cross-sectional areas at points AA and BB are equal (AA=ABA_A = A_B), the velocities at these two points will be equal (vA=vBv_A = v_B). In this case, the pressures at AA and BB will be equal. This makes the first option correct.
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