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