Analytical Formulae for the Approach Velocity Head Coefficient

Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

• Abdulrahman Abdulrahman

• Broad crested weir
• combined control meter
• control structures
• critical flow
• discharge measurement
• flow control
• hydraulic engineering
• hydraulic structures
• open channel flow.

[1] Abdulrahman, A. Direct solution to problems of open-channel transitions: rectangular channels, Journal of irrigation and drainage engineering, Vol. 134, No. 4, August 1, 2008, ASCE.
[2] Chow, V.T. (1958). Open channel hydraulics. McGraw-Hill Book Co. Inc., New York, N.Y.
[3] Douglas, E. John F, Gasiorek, Joseph M. and Swaffield, John A. (2001). Fluid Mechanics, P.545, 4TH ED., Pearson, Edinburgh Gate, England.
[4] Heading, J. (1970). Mathematical Methods in Science and Engineering, P. 40, 2ND Ed., Edward Arnold, London.
[5] Henderson, F.M. (1966). Open channel hydraulics. Macmillan Company, New York, N.Y.
[6] Streeter, Victor L. Wylie, E. Beniamin (1981), Fluid Mechanics, P. 475, 4TH Ed., Pearson, Edinburgh Gate, England.
[7] Sturm, Terry W. (2001). Open Channel Hydraulics, P. 33, 1ST Ed., McGraw-Hill C0mpany, Inc., 1221 Avenue of the Americas, New York, NY 10020.