I have 2 questions regarding the Bernoulli equation
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I would like to ask the teachers: In a continuous ideal fluid pipeline, according to Bernoulli’s equation: gz1 + P1/ρ + u1²/2 = gz2 + P2/ρ + u2²/2, ① are P1 and P2 determined only by the pipe diameter? ② If the pipe diameter changes, causing P1 and P2 to change, will the densities ρ at those two points also change? Thank you!
The Bernoulli equation is applicable to incompressible fluids, and this is a primary requirement. Furthermore, the pipe diameter generally depends on flow rate and is unrelated to pressure.
Dude, the diameter you mentioned actually affects the flow velocity as well as the height; so it’s not necessarily the case that the second value remains constant. The assumption behind Bernoulli’s equation is that the fluid is incompressible
①P1 and P2 are not only related to the pipe diameter but also to the height at which they are located. ② If the pipe diameter changes, P1 and P2 will change as well; however, the density ρ at those two points will remain unchanged
Thank you, I’d like to confirm the impact of pipe diameter on pressure
Well, the pipe diameter affects the flow velocity, and the flow velocity affects the static pressure. Why do P1, P2, and height have an impact? Isn’t the potential energy reflected in the expressions (gZ1, gZ2)? Thank you
Actually, I don’t know that much either. Bernoulli’s equation is a form of the law of conservation of energy; P1 and P2 are related to height, which are represented by gZ1 and gZ2. Perhaps what I’m saying isn’t what you mean. For a pipe of the same diameter, one part of it is on the horizontal surface while another part is at a height of 10 meters; by using a pressure gauge to measure the pressure difference between these two parts, the effect of height can be determined (ignoring pipeline resistance). In the case of water, the pressure difference would be 1000*9.8*10 Pa. If you’re referring to the static head of the same pipe at the same level, is it only related to the pipe diameter? I think so, if pipe resistance is ignored.
①P1 and P2 are independent of the pipe diameter. ② If the pipe diameter changes, P1 and P2 will change as well, but the density ρ at those two points remains unchanged
A change in pipe diameter affects the flow velocity; it should also affect the static pressure, right?
The pressure at the same level should be independent of the pipe diameter. The same is true for hydrostatics.
Dude, you’re not majoring in chemical engineering, are you?