Problem 6: Energy Equation DemonstrationRecently we saw a laboratory apparatus demonstrate several aspects of the energy equation. Asyou will recall, the cross-sectional area of the pipe varied from a maximum of 4.909×104 m² atpoint A to 7.854x105 m² at point E (factor of 6.25 difference):76.08BCDESLOB74355.0Part AWhat is the smallest velocity at Point E (VE) that will cause cavitation? T = 20°C, and you mayassume the pressure at Point A (PA) is one Denver atmosphere, so PA = Patm = 85 kPa. Neglectthe piezometer connections - assume they do not exist. [m/s]Part BIn reality, of course, we do have piezometer connections at points A-F. What happens in the realapparatus when the discharge equals the result from Part A? (≤25 words)

At point A and E,applying the continuity equation,given pressure at Cavitation: When the static…

Answered: Problem 6: Energy Equation…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

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Problem 6: Energy Equation Demonstration
Recently we saw a laboratory apparatus demonstrate several aspects of the energy equation. As
you will recall, the cross-sectional area of the pipe varied from a maximum of 4.909×104 m² at
point A to 7.854x105 m² at point E (factor of 6.25 difference):
76.08
BCDE
SLOB
74
35
5.0
Part A
What is the smallest velocity at Point E (VE) that will cause cavitation? T = 20°C, and you may
assume the pressure at Point A (PA) is one Denver atmosphere, so PA = Patm = 85 kPa. Neglect
the piezometer connections - assume they do not exist. [m/s]
Part B
In reality, of course, we do have piezometer connections at points A-F. What happens in the real
apparatus when the discharge equals the result from Part A? (≤25 words)

Expert Solution

Step 1: Part A):

At point A and E,

applying the continuity equation,

$straight A subscript straight A straight V subscript straight A equals straight A subscript straight E straight V subscript straight E 4.909 cross times 10 to the power of negative 4 end exponent straight V subscript straight A equals 7.854 cross times 10 to the power of negative 5 end exponent straight V subscript straight E straight V subscript straight E equals 6.250 straight V subscript straight A$

given pressure at $straight P subscript straight A equals 85 space KPa equals 85 cross times 10 cubed space straight N divided by straight m squared$

Cavitation: When the static pressure in the throat is lower than the vapor pressure of fine liquid a very rapid partial transition from liquid to gas phase occurs.

$straight P subscript Sat space 20 to the power of straight o straight C space equals space 2.339 space KPa The space pressure space must space be space jept space above space straight a space 2.339 space to space avoid space cavitation.$

By applying Bernoulli's equation at A and E

$fraction numerator straight P subscript straight A over denominator straight rho subscript straight w straight g end fraction plus fraction numerator straight V subscript straight A superscript 2 over denominator 2 straight g end fraction plus straight Z subscript straight A minus fraction numerator straight P subscript straight E over denominator straight rho subscript straight w straight g end fraction plus fraction numerator straight V subscript straight E superscript 2 over denominator 2 straight g end fraction plus straight Z subscript straight E equals 0 straight Z subscript straight A equals straight Z subscript straight E fraction numerator straight P subscript straight A minus straight P subscript straight E over denominator straight rho subscript straight w straight g end fraction minus fraction numerator straight V subscript straight E superscript 2 minus straight V subscript straight A superscript 2 over denominator 2 straight g end fraction fraction numerator 85 cross times 10 cubed minus 2.339 cross times 10 cubed over denominator 998.23 end fraction equals fraction numerator left parenthesis 6.25 space straight V subscript straight A right parenthesis squared minus straight V subscript straight A superscript 2 over denominator 2 end fraction 82.8 equals 19.03 space straight V subscript straight A superscript 2 straight V subscript straight A superscript 2 equals 4.35 straight V subscript straight A superscript blank equals 2.085 space straight m divided by straight s straight V subscript straight E equals 6.25 space straight V subscript straight A superscript blank straight V subscript straight E equals 13.03 space straight m divided by straight s$

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