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Old Jan 15th 2016, 05:02 AM   #1
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Pressure acting on wedge

1.) for the Sum of Fx , the author gave P1Δx - P3 (I sin theta) , why the author left off the sin theta at the below there ?
2.) Why the author assume Δz = 0 ? What's the purpose of assuming Δz = 0 ?

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Old Jan 15th 2016, 07:11 AM   #2
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Originally Posted by ling233 View Post
1.) for the Sum of Fx , the author gave P1Δx - P3 (I sin theta) , why the author left off the sin theta at the below there ?
Because it cancels out. Starting with equation (3-3a) sub in delta_x = l sin(theta) and you get:

P_1 l sin(theta) - P_3 l sin(theta) = 0, so:
P_1 - P_3 = 0.


Originally Posted by ling233 View Post
2.) Why the author assume Δz = 0 ? What's the purpose of assuming Δz = 0 ?
I must admit the author doesn't explain this very well, but it seems his purpose is to show that the pressure at a point (i.e. where delta_z = delta_x = delta_y = 0) is the same in all directions. So why doesn't he state that delta_x and delta_y also go to zero? Because those quantities have already cancelled out of the equations, so he ignores them.
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Old Jan 15th 2016, 07:52 AM   #3
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Originally Posted by ChipB View Post
Because it cancels out. Starting with equation (3-3a) sub in delta_x = l sin(theta) and you get:

P_1 l sin(theta) - P_3 l sin(theta) = 0, so:
P_1 - P_3 = 0.




I must admit the author doesn't explain this very well, but it seems his purpose is to show that the pressure at a point (i.e. where delta_z = delta_x = delta_y = 0) is the same in all directions. So why doesn't he state that delta_x and delta_y also go to zero? Because those quantities have already cancelled out of the equations, so he ignores them.
what do you mean by Because those quantities have already cancelled out of the equations, so he ignores them??
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Old Jan 15th 2016, 10:14 AM   #4
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Originally Posted by ling233 View Post
what do you mean by Because those quantities have already cancelled out of the equations, so he ignores them??
Do the math! Starting with equation (3-3b), replace the "l cos(theta)" term with delta_x, then divide through by delta_x.
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Old Jan 15th 2016, 05:26 PM   #5
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Originally Posted by ChipB View Post
Because it cancels out. Starting with equation (3-3a) sub in delta_x = l sin(theta) and you get:

P_1 l sin(theta) - P_3 l sin(theta) = 0, so:
P_1 - P_3 = 0.




I must admit the author doesn't explain this very well, but it seems his purpose is to show that the pressure at a point (i.e. where delta_z = delta_x = delta_y = 0) is the same in all directions. So why doesn't he state that delta_x and delta_y also go to zero? Because those quantities have already cancelled out of the equations, so he ignores them.
how about pressure at othert point other than delta_z = delta_x = delta_y = 0 ? are the pressure same at all direction ?
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Old Jan 15th 2016, 06:49 PM   #6
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Your question makes no sense. By definition a point has zero dimension, so delta-x = delta-y = delta_x = 0 for ALL points.
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