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The flow velocity in a 6-in. diameter pipe is twice that in a 12-in diameter pipe if both are carrying 50 gal/min of water. Solve it mathematically before you answer.

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Final answer:

In fluid dynamics, the speed of a fluid flowing through a pipe is inversely proportional to the cross-sectional area of the pipe. So, if the flow velocity in a 6-inch diameter pipe is twice that in a 12-inch diameter pipe, then the cross-sectional area of the smaller pipe is half of that of the larger pipe. This means that the flow velocity in the larger pipe is 1/4th of the velocity in the smaller pipe.

Step-by-step explanation:

In fluid dynamics, the speed of a fluid flowing through a pipe is inversely proportional to the cross-sectional area of the pipe. So, if the flow velocity in a 6-inch diameter pipe is twice that in a 12-inch diameter pipe, then the cross-sectional area of the smaller pipe is half of that of the larger pipe. This means that the flow velocity in the larger pipe is 1/4th of the velocity in the smaller pipe.

To solve it mathematically, we can use the equation:

V₁ / V₂ = A₂ / A₁

Where V₁ and V₂ are the velocities in the smaller and larger pipes, and A₁ and A₂ are the cross-sectional areas of the smaller and larger pipes, respectively.

Since the velocity in the smaller pipe is 12 m/s, and the velocity in the larger pipe is unknown, we can plug in the values to get:

12 / V₂ = (π * (6/2)^2) / (π * (12/2)^2)

Cancelling out the π and simplifying, we get:

12 / V₂ = (6/12)^2

12 / V₂ = 1/4

Cross-multiplying and solving for V₂, we find:

V₂ = 48 m/s

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