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Two pipes of diameters d1 and d2 converge to form a pipe of diameter 2d. If the liquid flows with a velocity of v1 and v2 in the two pipes, what will be the flow velocity in the third pipe?
  • a)
    v1 + v2
  • b)
    v1 + v2/2
  • c)
    v1 + v2/4
  • d)
    2(v1 + v2)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two pipes of diameters d1 and d2 converge to form a pipe of diameter 2...
Solution:

Given, diameters of two pipes as d1 and d2 and the diameter of the third pipe as 2d.

Let the flow velocity in the third pipe be v.

According to the principle of continuity, the volume of liquid flowing per unit time through the three pipes must be the same.

Mathematically,

v1 * A1 = v2 * A2 = v * A3

where A1, A2, and A3 are the cross-sectional areas of pipes 1, 2, and 3 respectively.

The cross-sectional area of a pipe is proportional to the square of its diameter.

Mathematically,

A1 = π(d1/2)²

A2 = π(d2/2)²

A3 = π(2d/2)² = 4π(d²)

Substituting the values of A1, A2, and A3 in the continuity equation, we get

v1(d1/2)² = v2(d2/2)² = v(d²)

Simplifying the above equation, we get

v = (v1(d1/2)² + v2(d2/2)²)/d²

v = (v1d1² + v2d2²)/(4d²)

v = (v1/v2)(d1/d2)²(v2/4)

v = (v1v2/4)(d1/d2)²

v = v1v2/4(d2/d1)²

v = v1v2/4(1/(d1/d2)²)

v = v1v2/4(1/(d2/d1)²)

v = v1v2/4(1/(d2²/d1²))

v = v1v2/4(d1²/d2²)

v = v1v2/4(1/d2²)(d1²)

v = v1v2/4(d1²/d2²)

v = v1v2/4(4/1)

v = v1v2

Therefore, the flow velocity in the third pipe is v1v2/4. Hence, option C is the correct answer.
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Two pipes of diameters d1 and d2 converge to form a pipe of diameter 2...
Option C
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Two pipes of diameters d1 and d2 converge to form a pipe of diameter 2d. If the liquid flows with a velocity of v1 and v2 in the two pipes, what will be the flow velocity in the third pipe?a)v1 + v2b)v1 + v2/2c)v1 + v2/4d)2(v1 + v2)Correct answer is option 'C'. Can you explain this answer?
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