 21 Sep 2022
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Crump Weir
 Updated on 21 Sep 2022
 3 Minutes to read

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The Crump Weir models a triangular profile weir with a 1:2 sloping front face and a 1:5 sloping back face.
Data
Field in Data Entry Form  Description  Name in Datafile 

Calibration Coefficient  Calibration coefficient (should be set to unity for most cases)  C_{c} 
Breadth of Weir  Breadth of weir at crest (m)  b 
Elevation of Weir  Elevation of weir crest (m above datum)  z_{c} 
Modular Limit  If Calculation Method set to FIXED, then a fixed modular limit value (eg 0.8) specified will be used; if set to VARIABLE (m=0 or blank in the dat file) then an internally calculated value will be used  m 
Upstream Crest Height  Height of crest above bed of upstream channel (m)  p_{1} 
Downstream Crest Height  Height of crest above bed of downstream channel (m)  p_{2} 
Upstream Node  Upstream node label  Label1 
Downstream Node  Downstream node label  Label2 
Upstream Remote Node  Upstream remote node label (must be a river or conduit section)  use if Label1 is not a river or conduit section  Label3 
Downstream Remote Node  Downstream remote node label (must be a river or conduit section)  use if Label2 is not a river or conduit section  Label4 
Theory and Guidance
The Crump Weir models a triangular profile weir with a 1:2 sloping front face and a 1:5 sloping back face.
Crump weirs are used as measuring structures in open channels and have the advantage that the coefficient of discharge is predictable and that the downstream bed elevations have little effect on modular limits and modular coefficient, for one in two upstream and one in five downstream sloping faces.
The design was originally prepared by Crump in 1952 and further investigated by W.R. White. The equations applied here are taken from White W.R. (1971); coefficient of discharge is taken from Fig.5 and the drowned flow reduction factor from Fig.11 (based on the curve for the ratio of upstream and downstream total head with no truncation of the weir).
It must be noted that the Crump Weir operates in terms of total head and requires that the upstream and downstream nodes are conduit or river sections, from whence the velocities are determined to calculate total head; if not, for instance if either node is attached to a junction., then remote upstream and/or downstream nodes may be specified from which to obtain a representative velocity.
Equations
y_{1 }³ y_{2 }(forward flow) h_{1} = h_{u} , etc
y_{1 }< y_{2 }(reverse flow) h_{1} = hd , etc
h_{1} = y_{1 } z_{c}
h_{2} = y_{2 } z_{c}
h_{u }= upstream head
h_{d }= downstream head
Mode 0  Dry Crest
Condition  y_{1 }< z_{c} y_{2 }< z_{c}  
Equation 

Mode 3  Free Flow
Condition  y_{1} < z_{c} or y_{2} < z_{c} H_{2}/H_{1} ≤ m where: m is the modular limit  
Equation 
where: C_{d} = discharge coefficient g = gravitational acceleration (m/s^{2}) H_{1} = h_{1} + v_{1}2/2g H_{2} = h_{2} + v_{2}2/2g with: v_{1} = upstream flow velocity v_{2} = downstream flow velocity 
Mode 4  Drowned Flow
Condition  y_{1} > z_{c} H_{2}/H_{1} > m where: m is the modular limit  
Equation 
where: C_{d} = modular discharge coefficient f_{r} = drowned flow reduction factor g = gravitational acceleration (m/s^{2}) H_{1} = h_{1} + v_{1}2/2g H_{2} = h_{2} + v_{2}2/2g with: v_{1} = upstream flow velocity v_{2} = downstream flow velocity 
General
A warning is generated if the Crump Weir is not attached (either directly or remotely) to nodes which have cross sections from which velocities can be established.
The routine allows reverse flow but applies the same equation (it assumes that the upstream face has a slope of one in five and the downstream sloping face is one in two). In practice it is unlikely that reverse flow will occur over a Crump Weir unless it has been sited badly.
If the weir complies with the British Standard and is free from blockages the calibration coefficient should be set to unity.
Datafile Format
Line 1  Keyword 'CRUMP' [comment]
Line 2  Label1, Label2, Label3, Label4
Line 3 
Line 4  p_{1}, p_{2}
Example
CRUMP
UNIT029 UNIT030
0.900 10.000 1.000 0.900
1.000 2.000