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Problem 3.60 PDF

The force of water on a plug sealing a conduit is calculated using hydrostatics equations. The magnitude of the force is 2.12 x 104 lbf directed to the right and perpendicular to the plug with its line of action located at a height of 12.19 ft above the bottom of the conduit.

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164 views1 page

Problem 3.60 PDF

The force of water on a plug sealing a conduit is calculated using hydrostatics equations. The magnitude of the force is 2.12 x 104 lbf directed to the right and perpendicular to the plug with its line of action located at a height of 12.19 ft above the bottom of the conduit.

Uploaded by

Kauê Britto
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Problem 3.

60 [Difficulty: 2]

lbf
Given: Plug is used to seal a conduit. γ = 62.4⋅
3
ft

Find: Magnitude, direction and location of the force of water on the plug.

Solution: We will apply the hydrostatics equations to this system.

Governing Equations: dp
=γ (Hydrostatic Pressure - y is positive downwards)
dh
FR = pc ⋅ A (Hydrostatic Force)

Ixx
y' = yc + (Location of line of action)
A ⋅ yc

Assumptions: (1) Static fluid


(2) Incompressible fluid
(3) Atmospheric pressure acts on the outside of the plug.
π 2
Integrating the hydrostatic pressure equation: p = γ⋅ h FR = pc⋅ A = γ⋅ hc⋅ ⋅ D
4

lbf π 2 4
FR = 62.4⋅ × 12⋅ ft × × ( 6⋅ ft) FR = 2.12 × 10 ⋅ lbf
3 4
ft

π 4
⋅D 2 2
π 4 64 D ( 6⋅ ft)
For a circular area: Ixx = ⋅ D Therefore: y' = yc + = yc + y' = 12⋅ ft +
64 π 2 16⋅ yc 16 × 12⋅ ft
⋅ D ⋅ yc
4
y' = 12.19⋅ ft

The force of water is to the right and


perpendicular to the plug.

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