Q = 2⁄3 cb √2g { (h2 + ɧ)3/2 − (h1 + ɧ)3/2 }.
(1)
And for a rectangular notch for which h1 = 0, the discharge is
Q = 2⁄3 cb √2g { (h2 + ɧ)3/2 − ɧ3/2 }.
(2)
In cases where u can be directly determined, these formulae give the discharge quite simply. When, however, u is only known as a function of the section of the stream in the channel of approach, they become complicated. Let Ω be the sectional area of the channel where h1 and h2 are measured. Then u = Q/Ω and ɧ = Q2/2g Ω2.
This value introduced in the equations above would render them excessively cumbrous. In cases therefore where Ω only is known, it is best to proceed by approximation. Calculate an approximate value Q′ of Q by the equation
Q′ = 2⁄3 cb √2g {h23/2 − h13/2 }.
Then ɧ = Q′2/2gΩ2 nearly. This value of ɧ introduced in the equations above will give a second and much more approximate value of Q.
| Fig. 49. |