Question

water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 1/4 of its previous value. if the speed of the water in the larger section of the pipe was 12 m/s, what is its speed in this smaller section? give your answer in m/s but do not include the units in the answer box.

Answer 1

To find the water speed in the smaller section of a pipe when the diameter decreases to 1/4 of the original, apply the continuity equation from fluid dynamics. The speed increases by a factor equal to the inverse of the square of the diameter decrease, resulting in a new speed of 192 m/s.

Step-by-step explanation:

The question involves the concept of the continuity equation from fluid dynamics, which states that the product of cross-sectional area (A) and velocity (v) remains constant for an incompressible fluid in steady flow (A1v1 = A2v2).

If the diameter of a pipe decreases to 1/4 of its original size, the radius will decrease to 1/4 as well, meaning that the cross-sectional area will decrease to (1/4)^2 = 1/16 of its original size.

To conserve the flow rate (volume per time), the velocity must increase by a factor that compensates for this decrease in area.

Therefore, if the original speed is 12 m/s, the new speed in the smaller section will be 12 m/s multiplied by 16 (the inverse of 1/16), giving us a speed of 192 m/s.