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.

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Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.5P: Evaluate the dimensionless groups hcD/k,UD/, and cp/k for water, n-butyl alcohol, mercury, hydrogen,...
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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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