For this problem, can you explain why they are are R^2-1/4piR^2*L for the volume part of the equation of weight? (The part circled in blue)

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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For this problem, can you explain why they are are R^2-1/4piR^2*L for the volume part of the equation of weight? (The part circled in blue)
Compute the horizontal and vertical components of the
hydrostatic force on the quarter-circle panel at the
bottom of the tank as shown in the figure.
Solution
F₁
W
Fy
FH = Fx
Fy = Fy + W
Water
W = mg = p * vol * g = 1000 *
2 m
Fx = p g hc * A=1000 * 9.81 * (5+2/2) * (2*6) = 706.32 KN
Fy=pg hc * A == 1000 * 9.81 * 5 * (2*6) = 588.6 KN
+ [(2² − ²1 (π 2²)) + 6] +
6 m
FH = Fx = 706.32 KN
Fy = Fy + W = 588.6 + 42.2 = 630.8 KN
5 m
2m
* * 9.81 42.2 KN
Transcribed Image Text:Compute the horizontal and vertical components of the hydrostatic force on the quarter-circle panel at the bottom of the tank as shown in the figure. Solution F₁ W Fy FH = Fx Fy = Fy + W Water W = mg = p * vol * g = 1000 * 2 m Fx = p g hc * A=1000 * 9.81 * (5+2/2) * (2*6) = 706.32 KN Fy=pg hc * A == 1000 * 9.81 * 5 * (2*6) = 588.6 KN + [(2² − ²1 (π 2²)) + 6] + 6 m FH = Fx = 706.32 KN Fy = Fy + W = 588.6 + 42.2 = 630.8 KN 5 m 2m * * 9.81 42.2 KN
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