Question

can someone solve this with full steps

A fluid flows upward in a conical contraction, and a U-tube manometer measures the pressure difference between the entrance and the exit, as shown in Figure 2. The flowing fluid has a density p and the heavier fluid in the manometer has a density p. The diameter at the entrance and exit are D, and D2, respectively. If the difference in the heights of the liquid interfaces in the manometer legs is h, derive an expression for h in terms of the flow rate Q and other variables of the system (h is shown to be zero in the Figure, when Q=0). Friction losses can be assumed to be negligible. (-) + O

Answer 1

& Let Latible length: =h2 h1 difference in height using Bernoulli's equatim P + 1 40² + Igh, = P2 + 1 1 0 77 4ghz Scanned with CamScanner

From contrunity equation me get foow thate, G= A v = A202 sh Алем 4 2 گرا respectively v2 cleanly od > A2 o į N27" and high y speed of How at 1 and 2 respectively 0 From (6) we can say that Pi>P2 so using Manometer] P, P2 = Sm gh P, - P₂ + 2 gro, 2 + 4 gh, = ₂10 2t 99 h ? (Im gh) + ² Ju, ? + Jgh, = ŽIr + 4 ghz Im gh + + 40,2 = £102² +48 (22-2) "Im gh ++, 120,2 = 1 40 2 2 + 19h Scanding = 1 0 2 - - 2 10 ² tyg 2

from G ID- diameter taren A = 1² = ID Angou a huge to ]4894 Jus eu e Leo Don]* en [Length I the pipe required) Scanned with CamScanner