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Water is flowing in a pipe as shown in the figure. If the diameter of the pipe at point 1 and point 2 are D and 2D respectively, then find the ratio of the velocity of the water at point 1 to point 2.

  1. 1 : 2
  2. 2 : 1
  3. 1 : 4
  4. 4 : 1

Answer (Detailed Solution Below)

Option 4 : 4 : 1
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Detailed Solution

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CONCEPT:

Continuity equation:

  • According to the continuity equation, the mass flow rate at every point in the fluid flow remains constant.

⇒ ρ1A1v1 = ρ2A2v2

  • If the flow is incompressible i.e. ρ1 = ρ2,

⇒ A1v1 = A2v2

Where ρ1 = density of fluid at point 1, A1 = area of cross-section at point 1, v1 = velocity of fluid at point 1, ρ2 = density of fluid at point 2, A2 = area of cross-section at point 2, and v2 = velocity of fluid at point 2

CALCULATION:

Given d1 = D and d2 = 2D

  • Area of the pipe at point 1,

  • Area of the pipe at point 2,

According to continuity equation,

⇒ A1v1 = A2v2

  • Hence, option 4 is correct.

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