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posted by  EEHW on 9/22/2008 10:22:18 PM  |  status: Live  

Fluid Mechanics

Course Textbook Chapter Problem
Fluid Mechanics N/A N/A N/A
Question Details:
Three gates of negligible weight are designed to hold back water in a channel as shown below. Channel depth h=3m. The force of the gate against the block per unit width (B =1m) of channel is given by R for design (b).
i) Determine the magnitude of R.

ii) Express the force against the block for design (a) and (c) in terms of R.

iii) Briefly explain the difference in force for the three designs.
 
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posted by EngAve on 10/4/2008 1:40:59 PM  |  status: Live
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Response Details:
I.)



Answer: R = 29.43kN
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posted by EngAve on 10/4/2008 2:03:05 PM  |  status: Live
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Response Details:
II.)
For gate (a):

applied at from point directly above the vertical section of the gate.
applied at 2m below water head.
Taking sum of all moments about the hinge H, in equilibrium:

So, we can calculate
But we want the force in terms of the resultant R, so:
Answer: FB = 1.17 R
For gate (c):
Resultant force of water on the bottom half of the gate (where the gate is straight):

Resultant force of water on the top half of the gate (where teh gate is straight) is directed at the hinge (point H), and therefore it's moment about point H will be zero.  So, we can take the sum of all moments about the hinge H, in equilibrium:

So, we can calculate
But once again, we want the force in terms of the resultant R, so:
Answer: FB = 0.874 R
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posted by EngAve on 10/4/2008 2:06:37 PM  |  status: Live
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Response Details:
III.)
The only difference between the three gates takes place in the upper half of each gate, where we go from a concave section, to flat, to convex.  The vertical component of the hydrostatic force pushes further into gate (a), and creates the highest water pressure in this instance.  In gate (c), the opposite effect takes place, and the hydrostatic water pressure is taken on by the hinge H, leaving gate (c) as the least pressured gate of all three examples.  Therefore, the only difference is the vertical component of the hydrostatic force.
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