Answered: The water flows to the nozzle through a…

Name: The water flows to the nozzle through a 180-degree elbow. The pipe dia
Uploaded: 2024-03-20T06:56:55.000Z
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Description: The water flows to the nozzle through a 180-degree elbow. The pipe diameter D-75mm, the nozzle diameter d=25mm, and the pressure gauge at the front of the pipe reads 60kPa. Find the force of the upper, middle and lower bolts at the flange joint 1-1 p

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The water flows to the nozzle through a 180-degree elbow. The pipe diameter D-75mm, the nozzle diameter d=25mm, and the pressure gauge at the front of the pipe reads 60kPa. Find the force of the upper, middle and lower bolts at the flange joint 1-1 position. Assuming that four bolts are installed at the up, down, front and back, the cross-center distance of the four bolts is 150mm, the weight of the elbow and the water is 100N, and the acting position is shown in the figure.

Please use conservation of momentum (momentum equation) and draw the control volume since that is our lesson.

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Good day. Can you please inspect my solution. Is it wrong? I used the summation of forces=momentum change.

Step 3
Solve for the horizontal force acting on the bolt (F₁) using momentum equation:
F₁ Horizontal force or momentum change
m=mass
Av = velocity change
Fh=m Av
AV= (V1-V2)
V2 should be negative because it has opposite direction to v₁
Av= (v2--V1) = (v1+V2)
m=(pAv₁)
-P1A1 - P₂A2+ Fh= (pA1V₁) (V₁+V2)
-60×10³((0.075 )² -0 + F₁ =1000 ((0.075 )²(1.254+11.29)
Fh= 1000 ((0.075)²(1.254)(1.254+11.286) + 60x10³((0.075)²
Fh=334.59 N
Solve for the vertical force acting on the bolt:
FvFw=0
Fv-100N=0
Fv = 100 N
Solve for the total force acting on the bolt (Fr):
Fv=100 N (weight due to elbow and water)
Fh=334.59 N (horizontal force on bolt)
FT-Total force on bolt
2
FT= √F_²+F²
H
FT=√(334.59)²+(100)²
FT 349.21 N
Solve for the force acting on each bolt:
N=4 (4 bolts)
F= force on each bolt
F=
F₁
4
349.21
4
F=87.30 N
F=
Conclusion:
Force on each bolt is 87.30 N.

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