Discussion on Question 15 from the 2018 case study in the morning
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This post was last edited by GorgeousYue on 2019-4-30 08:41. After determining the vacuum level at point B in this problem, is it necessary to take into account the vacuum resulting from a liquid level of 0.5 m as well? ? ? The figure accompanying the question indicates that the distance from the vacuum gauge to point B is 0.5 m. The vacuum degree difference is 5.886 kPa
The vacuum level in the pressure gauge should be lower than that at point B
15【Analysis】 For plane D, apply Bernoulli’s equation using planes A and C: Z1 + P1/pg + u1^2/2g + H = Z2 + P2/pg + u2^2/2g + (z*L/D + S)*u^2/2g. Here, gauge pressure is used; z1 = 0, Z2 = 16, P1 = P2 = 0, u2 = u1 = 0. The local resistance velocity is the velocity within the pipeline. 12/1000 = 0.785*0.08^2*u, so u = 2.39 m/s. Then, H = 16 + (0.04*(20 + 5)/0.08 + (0.17 + 0.88 + 2*1.0 + 0.75 + 6.4 + 2.0 + 5*0.75) + 0.5 (inlet) + 1.0 (exit)) * 2/39^2/2/9.81, which gives H = 24.72 m. Applying Bernoulli’s equation using plane A and the vacuum gauge, we get: P (gauge pressure)/pg = 2 + (0.04*(5 + 0.5)/0.08 + (0.17 + 0.88 + 2*1.0 + 0.75 + 0.5 (suction)) * 2.39^2/2/9.81, resulting in P (gauge pressure) = 47 KPaG. The vacuum level is equal to -P (gauge pressure). Therefore, the correct answer is (D). This is a relatively basic question in hydraulic calculations and one that is asked every year. It is important to take into account the resistance losses at the inlet and outlet; otherwise, it is impossible to obtain the correct answer.
I’m a bit confused: will the section from point B to the base of the vacuum gauge (0.5 m) be filled with liquid? It seems to be in a negative pressure state; should it not rather be filled with air?