**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3

# Publications

##### 3 Analytical Formulae for the Approach Velocity Head Coefficient

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

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.

**Keywords:**
Broad crested weir,
combined control meter,
control structures,
critical flow,
discharge measurement,
flow control,
hydraulic engineering,
hydraulic structures,
open channel flow.

##### 2 Numerical Solution of Manning's Equation in Rectangular Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

**Keywords:**
Channel design,
civil engineering,
hydraulic engineering,
open channel flow,
Manning's equation,
normal depth,
uniform flow.

##### 1 General Formula for Water Surface Profile over Side Weir in the Combined, Trapezoidal and Exponential, Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

**Keywords:**
Analytical solution,
combined channel,
exponential channel,
side weirs,
trapezoidal channel,
water surface profile.