- #1
kubaanglin
- 47
- 5
Homework Statement
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When the level of water in a reservoir is too high, the water spills out over a spillway,
as illustrated in the figure below
Neglecting viscosity, show that the water flow ##Q## over the spillway is given by
$$Q=\frac{2}{3}w\sqrt{2gy^3}$$
Homework Equations
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Bernoulli's Equation: ##P_1+\rho gh_1+\frac{1}{2}\rho v_1^2=P_2+\rho gh_2+\frac{1}{2}\rho v_2^2##
Torricelli's Equation: ##v=\sqrt{2gh}##
The Attempt at a Solution
##Q=Av=(wy)(\sqrt{2gy})=w\sqrt{2gy^3}##
I am not sure how to get ##\frac{2}{3}## in this equation as indicated by the answer. I feel that I am oversimplifying this by assuming the height in Torricelli's equation is just ##y## when it should account for flow over an area as opposed to a point. Would this mean the height is ##\frac{y}{2}## to get the average velocity of the fluid?