Hi everybody! I'm training for an upcoming exam, and I'd like to know if I correctly use the Bernoulli equation. 1. The problem statement, all variables and given/known data The problem is kind of difficult to describe without a drawing, please check out the attached jpg to see the situation and the known data. The questions are: a) How much time t is needed for a volume V = 1L of fluid to cross the hopper? b) What is the diameter of d2? 2. Relevant equations Bernoulli equation, equation of continuity, formulas to calculate the flux of a fluid 3. The attempt at a solution a) I use the Bernoulli equation at points (1) and (0): P1 + ρgh1 + ½ρv12 = P0 + ρgh0 + ½ρv02 Now I think that P1 = 0 (if we take the gauge pressure), ½ρv12 ≈ 0 (because the diameter at point (1) is much larger than at point (0) (equation of continuity)) and ρgh0 = 0 (because I choose h0 = 0). What I am not sure of is that I assume P0 = 0 because the fluid is not being stopped at that point, so it should have no pressure. Is that correct? If so, here is where that takes me: ρgh1 = ½ρv02 ⇔ v0 = √(2gh1) We can then use the flux to determine the time it takes for a litre of fluid to cross the hopper: R = V/t = A0 ⋅ v0 ⇒ t = V/(¼ ⋅ π ⋅ d02 ⋅ √(2⋅g⋅h1)) = 23.5 s b) I use the Bernoulli equation again at points (0) and (2). P0 + ρgh0 + ½ρv02 = P2 + ρgh2 + ½ρv22 I assume P0 = 0 and P2 = 0 for the same reason as before (is that right?) and ρgh2 = 0 (because I now choose h2 = 0) ⇒ v2 = √(v02 + 2⋅g⋅h0) The equation of continuity says A0 ⋅ v0 = A1 ⋅ v1 ⇒ A2 = A0 ⋅ v0/v2 ⇒ r = 1.5 mm ⇒ d2 = 3 mm My results are plausible, but I am unsure about how to deal with the pressure when there is a flow. Is there no pressure on the right side of the equation when there is a flow? Is that always the case? Thank you very much in advance for your answers.