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Water flows inside a solid cylindrical pipe, which narrows as it goes up to a height h (see diagram below). The lower horizontal section has circular cross-sectional diameter d, whereas the upper horizontal section has diameter d/2. Let us denote A to be a point at the lower horizontal section and B to be a point at the upper horizontal section. The flow speed at A and B is uд and uâ, respectively. The pressure at A and B is PA and PB, respectively.

Water flows inside a solid cylindrical pipe, which narrows as it goes up to a height h (see diagram below). The lower horizontal section has circular cross-sectional diameter d, whereas the upper horizontal section has diameter d/2. Let us denote A to be a point at the lower horizontal section and B to be a point at the upper horizontal section. The flow speed at A and B is uд and uâ, respectively. The pressure at A and B is PA and PB, respectively.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Water flows inside a solid cylindrical pipe, which narrows as it goes up to a height h (see diagram below). The lower horizontal section has circular cross-sectional diameter d, whereas the upper horizontal section has diameter d/2. Let us denote A to be a point at the lower horizontal section and B to be a point at the upper horizontal section. The flow speed at A and B is uд and u, respectively. The pressure at A and B is PA and PB, respectively. РА UA Oom Ja d d/21 1 UB h (a) Assuming water to be incompressible, show that the flow speed at B is four times the flow speed at A. (b) Use Bernoulli's equation to find the drop in the water pressure from A to B. Express the result in terms of h, uд, the density of water p, and the acceleration of gravity g. (c) Above certain critical height h, vapour bubbles start to appear at the top horizontal section, which hinders water flow through the pipe. Explain why this happens.
Transcribed Image Text:Water flows inside a solid cylindrical pipe, which narrows as it goes up to a height h (see diagram below). The lower horizontal section has circular cross-sectional diameter d, whereas the upper horizontal section has diameter d/2. Let us denote A to be a point at the lower horizontal section and B to be a point at the upper horizontal section. The flow speed at A and B is uд and u, respectively. The pressure at A and B is PA and PB, respectively. РА UA Oom Ja d d/21 1 UB h (a) Assuming water to be incompressible, show that the flow speed at B is four times the flow speed at A. (b) Use Bernoulli's equation to find the drop in the water pressure from A to B. Express the result in terms of h, uд, the density of water p, and the acceleration of gravity g. (c) Above certain critical height h, vapour bubbles start to appear at the top horizontal section, which hinders water flow through the pipe. Explain why this happens.
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