# Fluid Mechanics Question - Angled Sluice Gate

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_2bsqrt(2g(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!

My first post had an error, which has been corrected below:

I have another question on this assignment. I have a problem involving a Venturi Flume. The initial height of the water is 1.2m with a velocity labeled V_1, and there is a rise of 0.2m on the ground coinciding with a drop of 0.07m in the height of the water (directly over the bumb, the top dips down that much compared to the previous height). The velocity here is labeled V_2. Assuimg inviscid fluid and the velocity is uniform, what is the flowrate per width of the channel?

I was doing this problem and kept coming up with an answer that involved the term V_1. Since the problem gives numerical heights, I assume the answer is expected to also be numerical. My strategy was to first put the second velocity in terms of the first velocity using Q = VA at both points, holding Q constant. I then found the pressure difference, in terms of V_1 by using the Bernoulli equation. I then put this result (P_1 - P_2) into an equation found in the book that models the flow rate in this situation, Q = A_2 * sqrt(2(P_1 - P_2)/(rho*[1-*(A_2 / A_1)^2])). Of course, puting the pressure brings V_1 into the equation, and I cannot see a way to avoid it.

I dont wont to do your homework, but

I’m trying to find flowrate, not the force on the sluice gate. The link also mentions nothing about the angle of the sluice gate and how to factor that into the equations. I shall ask someone in class today and hopefully I’ll be able to quickly do the problem.

I found out that the flowrate is independent of the sluice gate, so the equation in the book was all I needed. For the other problem, I used two points at the surface of the water, one where it’s wide and one where it’s narrower. The pressures will both be 0, and the change in elevation is known. I can put one velocity in terms of the other and solve for the second velocity, then multiply that by the area per unit width to figure out the flowrate.