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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.

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.

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
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.

300 mm 300 mm 100 N Рм 2 2 2
Transcribed Image Text:300 mm 300 mm 100 N Рм 2 2 2
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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.
Transcribed Image Text: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.
ΣFx = P₁A₁ - R = pQ(V₂ — V₁)
Transcribed Image Text:ΣFx = P₁A₁ - R = pQ(V₂ — V₁)
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