17. A big pipeline branches into 6 other small pipes (same diameters, same length and same geometric plane). Will the flow rates and velocity of the small pipes be the same? (1) A) Yes, according to the continuity equation the flow rate in each branch will be 1/6 of the total flow rate. B) Yes, according to the continuity equation the flow rate in each branch will be 6/1 of the total flow rate. C) No, according to the continuity equation, the flow rate in each branch will be 1/6 of the total flow rate. D) The information given is not enough to respond to the question.
Question
- A big pipeline branches into 6 other small pipes (same diameters, same length and same geometric plane). Will the flow rates and velocity of the small pipes be the same? (1) A) Yes, according to the continuity equation the flow rate in each branch will be 1/6 of the total flow rate. B) Yes, according to the continuity equation the flow rate in each branch will be 6/1 of the total flow rate. C) No, according to the continuity equation, the flow rate in each branch will be 1/6 of the total flow rate. D) The information given is not enough to respond to the question.
Solution
The correct answer is A) Yes, according to the continuity equation the flow rate in each branch will be 1/6 of the total flow rate. The continuity equation in fluid dynamics states that the mass flow rate must remain constant from one cross-section of the pipe to another, assuming no fluid is added or removed. Therefore, if a big pipeline branches into 6 smaller pipes of the same diameter and length, the flow rate in each of the smaller pipes will be 1/6 of the total flow rate.
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