When applying Bernoulli’s equation, under what conditions is the velocity “u1” equal to zero or approximately zero?
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When studying the textbooks from Tianjin University and the exercise sets provided by the association, one encounters situations where the velocity u1 at section 1-1 is given to be approximately 0 or exactly 0. This can be seen in Example 3.1-7 on page 93 and Example 3.1-9 on page 95 of Tianjin University’s professional textbooks, as well as in exercises 3-31 and 3-34 in the association’s exercise sets. I spent so much time trying but still didn’t understand it. If we understand V as uA, then the flow rate remains constant and the cross-sectional area is infinite; thus, if u is approximately 0, why can’t the velocity at the pump inlet also be approximated as 0? After all, the pump draws water from a tank with a very large cross-sectional area as well. I’m sorry for the inconvenience; I’m not very smart. I hope everyone can offer some guidance. Thank you
It’s the water level in the pool, not the pump inlet, right?
The two are the same reference cross-section; both are the surface of the pool
When the shut-off valve on the pipeline is closed, U1 becomes 0.
If you have time, could you please help check the answers to questions 3-37 in the association’s problem set? When applying Bernoulli’s equation between sections 1-1 and 2-2, both u1 and u2 are non-zero; however, when applying Bernoulli’s equation between section 1-1 and section C-C, as well as between section 2-2 and section D-D, u1 is zero. Why is that? Thank you
The question does not address the closing of valves. Thank you for your participation
Personally, I think there are indeed some issues with the solution to this problem, especially regarding the calculation of u2. Since the local resistance at the pipe outlet at point G has already been taken into account, it should indeed be the liquid level in the sump that serves as the reference section for calculation; the flow velocity at this section definitely should not be the same as that at the inside of the pipe outlet.
Questions 3-31 and 3-34 in the association’s* question set are fine; using the liquid surface of the large container as the calculation cross-section results in a flow velocity of 0, which is essentially zero in reality. If the cross-section is taken at the inside of the outlet pipe leading into the container, then the flow velocity is equal to that within the pipe. Generally, there are two options when selecting section 2: if the inner side of the pipe opening is chosen, the kinetic energy term is non-zero while the local resistance term at the pipe opening is zero; if the outer side of the pipe opening is chosen, the kinetic energy term is zero while the local resistance term at the pipe opening is non-zero.
I agree with what was said above, but I think there are some issues with the solution to this problem. The flow velocities at sections 1-1 and 2-2 should both be 0. When applying Bernoulli’s equation between 1-1 and 2-2, u1 and u2 represent the flow velocities at the inlet and outlet of the pump, not those at sections 1-1 and 2-2; these values are used to calculate the pipe resistance. At this point, the kinetic energy term in the solution should not be expressed using u1 and u2, as this can lead to confusion.
Thank you for your answer. But the answers to questions 3-37 in the association’s question set aren’t done this way; please take a look and give me some guidance
Well, I already replied above that the answer to question 37 seems to have some issues; it might also be due to a lack of thorough understanding on our part. The flow rate mentioned refers to the flow rates at the inlet and outlet of the pump, which is hard to understand. But errors in the association’s books are common, so there’s no need to worry too much about it.