Engineering Flow through hinged hatch on inclined wall

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The discussion focuses on deriving an expression for flow (Q) through a hinged hatch on an inclined wall. An initial equation using the orifice equation has been established, but it does not account for the angle of inclination. Participants suggest that the flow at the bottom can be related to the adjacent side of a triangle formed by the angle alpha. A trigonometric ratio is proposed as a potential method to express this bottom side. The conversation seeks further assistance in developing a comprehensive flow equation that incorporates the angle.
Kapper
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Homework Statement
I have a tank, where I want to determine the outflow through an orifice. The problem is that the orifice opening is controlled by a hatch with varying angles dependent on the sum of torques.
Relevant Equations
Orifice equation
1670797437614.png

So far I have only been able to come up with an equation for the flow (Q) using the orifice equation through the inclined area and thus not dependent on the angle.

Can someone help me with an expression for this?
 
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Would not the flow out the bottom be the adjacent side of triangle with angle alpha? You could use a trig ratio to express that bottom side.
 
Thread 'Why wasn’t gravity included in the potential energy for this problem?'

Thread 'Why wasn’t gravity included in the potential energy for this problem?'

I’m looking at the attached vibration problem. The solution in the manual includes the spring potential energy but does NOT include the gravitational potential energy of the hanging mass. Can someone explain why gravitational potential energy is not included when deriving the equation of motion? I tried asking ChatGPT but kept going in circles and couldn't figure out. Thanks!
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