## Orifice and Weir flow calculations

Note:  Orifice and Weir Flow Computations

The orifice flow calculation proceeds as follows:

1. Initially and whenever the setting (i.e., the fraction opened) changes, flow coefficients for both orifice and weir behavior are computed as follows:

a. For side orifices:

Define Hcrit = h/2 where h is the opening height.

b. For bottom orifices:

i. For a circular orifice, compute area over length (i.e., circumference) as AL = h /4.

ii. For a rectangular orifice compute AL = h*w/(2*(h+w)) where w is the opening width.

iii. Compute Hcrit = Cd*AL/0.414 where Cd is the orifice discharge coefficient.

At step 1b, the critical head for the bottom orifice, where orifice flow turns into weir flow, is found by equating the result of the orifice equation to that of the weir equation

Cd*Area*sqrt(2g)*sqrt(Hcrit) = Cw*Length*sqrt(Hcrit)*Hcrit or

Hcrit = (Cd * Area) / (Cw/sqrt(2g) * Length) The value of Cw/sqrt(2g) for a sharp crested weir is 0.414.

c. Compute the flow coefficients (where A is the area of the opening):

Corif = A*sqrt(2g)*Cd

Cweir = A*sqrt(2g)*Cd*sqrt(Hcrit)

2. During flow routing, compute the degree of inlet submergence (f) and head (H) at the current time step:

a. Define:

Hcrest = elevation of bottom of opening,

Hcrown = elevation of top of opening,

Hmidpt = elevation of midpoint of opening

b. For side orifices:

f = min{1.0, (H1 - Hcrest) / (Hcrown - Hcrest)}

if f < 1.0 then          H = H1 - Hcrest,

else if H2 < Hmidpt then H = H1 - Hmidpt

else                     H = H1 - H2

c. For bottom orifices:

if H2 > Hcrest then H = H1 - H2

else                H = H1 - Hcrest

f = min{1.0, H/Hcrit}

3. Compute the flow through the orifice (Q):

if f < 1.0 then Q = Cweir*f^1.5

else            Q = Corif*sqrt(H)

4: Villemonte correction

If f < 1.0 and H2 > Hcrest then:

r = (H2 - Hcrest) / (H1 - Hcrest)

Q = Q * (1 - r^1.5)^0.385

Weir Flow Computations

h1 = Upstream Node Depth + Upstream Invert Elevation

h2 = Downstream Node Depth + Downstream Invert Elevation

If h2 is greater than h1 then the flow is reversed and h2 = h1 and h1 = h2

Weir Crest = Upstream Node Invert Elevation + Weir Offset Depth

Head = h1 – Weir Crest

2.  Center Weir flow for Transverse Weirs

Q = Cw * Weir Length * Head^3/2

3.  Center Weir flow for Side Flow Weirs

Weir behaves as a transverse weir under reverse flow

Q = Cw * Weir Length * Head^3/2

And under normal flow

Q = Cw * Weir Length * Head^5/3

4.  Center Weir flow for V Notch Weirs

Q = Cw * Weir Slope * Head^5/2

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