My Fluid Mechanics book shows that the flow rate from a sluice gate depends on the height of the water before the sluice gate (z_1), the flow rate after the gate (z_1), the height of the opening that the gate allows (a) and the width of the gate (b). The equation for flow is Q = z_2*b*sqrt(2*g*(z_1-z_2)/(1-(z_2/z_1)^2)

My question is, how do I figure out the flow rate if the gate is tilted at an angle (theta) from the vertical? I assume there needs to be some sort of trig function added to the equation, but the book says nothing about what it should be, and my instructor didn’t go over it in lecture. Could someone just tell me how to work in the angle, and I’ll do the rest (I don’t want to violate the no doing homework rule). Thanks!