Question

At location 1 along the pipe, the flow speed is 9.97 m/s and the pipe diameter d1 is 10.1 cm. At location 2, pipe diameter d2 is 14.7 cm. At location 1, the pipe is?

1) Narrower than at location 2
2) Wider than at location 2
3) The same width as at location 2
4) Cannot be determined

Answer 1

At location 1, the pipe diameter is 10.1 cm and is narrower than at location 2, where the diameter is 14.7 cm.

Step-by-step explanation:

At location 1 along the pipe, the flow speed is 9.97 m/s and the pipe diameter d1 is 10.1 cm. At location 2, the pipe diameter d2 is 14.7 cm. Comparing the two diameters, we can see that at location 1, the pipe is narrower than at location 2 since 10.1 cm is less than 14.7 cm. Additionally, according to the principles of conservation of mass and the continuity equation, which states that the mass flow rate must be constant throughout the pipe, the velocity of the fluid will change inversely with the cross-sectional area (A = πd2/4) of the pipe. Hence, the fluid flows faster in narrower sections of the pipe than in wider sections.