Measurement of flow in supercritical flow regime using cutthroat flumes

Abstract

Cutthroat flume is commonly used for measurement of subcritical flow in open channel because of its simplicity and ease of construction. No experimental data is available in literature for measurement of flow in supercritical regime using cutthroat flume. The present paper finds the feasibility of cutthroat flume as a measurement device for flow in supercritical regime. Experimental data are generated to develop the relation between discharge and observed head at a specified location on upstream of throat section. Regression analysis for discharge and head indicated a good correlation. Based on all the experimental data generated, a relationship between discharge and head is proposed.

Appendices

Appendix A.

Measurement of discharge and head (when critical flow condition is observed at the throat section).

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Appendix B.

Measurement of discharge and head (under general condition of flow).

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Notation

L length of cutthroat flume (m)

g acceleration due to gravity (m/s ²)

N exponent of equation in free flow condition

Q discharge through flume in (m ³/s)

$Q^{\ast } =\frac {Q_{a}} {\sqrt g \times W^{2.5}}$ dimensionless discharge head for category I

R ² coefficient of determination

W throat width of cutthroat flume (m)

h _a head at location of depth measuring gauge (m)

S bed slope of rectangular flume

h _a/W dimensionless head

E* = E _a/W dimensionless total head for category I

B width of cutthroat flume (m)

C coefficient

C _d coefficient of discharge

K constant in discharge equation under free flow

Z _a datum head at head measurement point (m)

$\frac {{V_{a}^{2}}} {2g}$ velocity head at head measurement point (m)

h _b head at throat section (m)

$\frac {{V_{b}^{2}}} {2g}$ velocity head at throat section (m).

n exponent for category II

$E_{0}^{\ast }$ dimensionless total head for category II

$Q_{0}^{\ast }$ dimensionless discharge head for category II