Crump Weir | Technical Reference

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)	p₁
Downstream Crest Height	Height of crest above bed of downstream channel (m)	p₂
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

y₁³ y₂(forward flow) h₁ = h_u , etc

y₁< y₂(reverse flow) h₁ = hd , etc

h₁ = y₁- z_c

h₂ = y₂- z_c

h_u= upstream head

h_d= downstream head

Mode 0 - Dry Crest

Condition

y₁< z_c

y₂< z_c

Equation

Q = 0

(1)

Figure 1: Crump Weir parameters (slopes not to scale)

Mode 3 - Free Flow

Condition

y₁ < z_c or y₂ < z_c

H₂/H₁ ≤ m

where:

m is the modular limit

Equation

(2)

where:

C_d = discharge coefficient

g = gravitational acceleration (m/s²)

H₁ = h₁ + v₁2/2g

H₂ = h₂ + v₂2/2g

with:

v₁ = upstream flow velocity

v₂ = downstream flow velocity

Figure 2: Crump Weir (free flow)

Mode 4 - Drowned Flow

Condition

y₁ > z_c

H₂/H₁ > m

where:

m is the modular limit

Equation

(3)

where:

C_d = modular discharge coefficient

f_r = drowned flow reduction factor

g = gravitational acceleration (m/s²)

H₁ = h₁ + v₁2/2g

H₂ = h₂ + v₂2/2g

with:

v₁ = upstream flow velocity

v₂ = downstream flow velocity

Figure 3: Crump Weir (drowned flow)

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 - p₁, p₂

Example

CRUMP
UNIT029     UNIT030
     0.900    10.000     1.000     0.900
     1.000     2.000