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Old Jun 4th 2014, 10:20 AM   #1
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fluid mechanics (help pls)

Pls I need answers to this difficult assignment

A square aperture in the vertical side of a tank has one diagonal vertical and is completely covered by a plane plate hinged along one of the upper sides of the aperture. The diagonals of the aperture are 2m long and the tank contains a liquid of relative density 1.15. The center of the aperture is 1.5m below the free surface. Calculate the net hydrostatic thrust on the plate, the moment of this thrust about the hinge and the position of the center of pressure
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Old Jun 4th 2014, 10:24 AM   #2
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I need go get it done by the end of today... pls I need you Guy's help
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Old Jun 4th 2014, 11:41 AM   #3
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I jez need a start up....somebody pls tell me what to do
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Old Jun 4th 2014, 12:21 PM   #4
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To get started on the first part - the pressure is the integral of the incremental pressure across the surface of the plate:



where h = depth, w(h) = width of the plate at depth h. You will need to establish a formula for w as a function of h and calculate this integral.

For the second part I suggest a double integral in in dh and dw, together with a moment arm calculation depending on h and w:




where l(h,w) is the moment arm of the point (h,w) from the hinge.
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Old Jun 4th 2014, 12:27 PM   #5
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Tanks a lot....am I integrating twice with respect to w and h to get the moment?
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Old Jun 4th 2014, 12:28 PM   #6
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Wat about the centre of pressure
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Old Jun 5th 2014, 07:17 AM   #7
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Originally Posted by obas21 View Post
Tanks a lot....am I integrating twice with respect to w and h to get the moment?
It's a double integral - once with respect to dw and then with respect to dh.

Originally Posted by obas21 View Post
Wat about the centre of pressure
Divide the moment acting about the hinge by the total pressure acting on the plate - this gives you the distance from the hinge to the center of pressure. From symmetry you know it acts somewhere along the vertical diagonal.
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Old Jun 5th 2014, 02:12 PM   #8
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Pls, does differentiating twice means differentiating wrt h first or wat does it mean
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Old Jun 5th 2014, 02:14 PM   #9
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I'm still having difficulty getting it.....I need ur help pls
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Old Jun 6th 2014, 04:37 AM   #10
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Originally Posted by obas21 View Post
Pls, does differentiating twice means differentiating wrt h first or wat does it mean
It's a double integral, not differential. Have you taken any calculus courses? I assumed you had, but if not - where did you get this problem from?

Let's start with the first part of the problem - rather than use calculus you can use the fact that the total hydrostatic force acting on a vertical submerged plate is equal to the pressure at the plate's centroid times its area. Was that covered in your text book?

Last edited by ChipB; Jun 6th 2014 at 08:29 AM.
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