flow over rectangular and v - notches

Hydraulics Laboratory Experiment Report

Name:

Ahmed Essam Mansour

Section: "1", Monday 2-5 pm Title:

Flow over rectangular and v - notches

Date:

30 –October-2006

Objectives:

• To determine the coefficient of discharge for both rectangular and v – notches.

Theory: Weirs and notches are placed in the path of an open channel for two main reasons: 1. To measure flow rate in the channel, 2. To regulate flow rate. If the relationship between the water level upstream and the discharge is known, then the discharge at any time can be found by only knowing the height of water in the upstream of the weir. And so, by only knowing some properties of the weir the discharge can be controlled by controlling the water level at the upstream. From this experiment the relation between the flow rate and water level up stream is to be determined, by finding out two main coefficients related to the weir or notch; 1. Coefficient of discharge "Cd". 2. "n", which depend mainly on the shape of the notch. The general form of the equation defining the relation between the water level at the upstream of the notch and the rate of discharge is;

where; K: a function of the coefficient of discharge and the dimensions of the notch. H: the height of water at the upstream.

Theoretical analysis:

This is used to define the velocity of discharge at the notch in an expression with the water level upstream and the gravitational acceleration;

Then the velocity of discharge is expressed by;

where; h: the water level upstream, g: the gravitational acceleration (9.81 m/s). In our experiment we used a rectangular and V – notches, and they were theoretically analyzed as follows;

For a rectangular notch:

For a V – notch:

The obtained relations between "Q" and "H", represent the theoretical results based on calculations, but the actual relation would be different; more specifically the actual flow rate would be less than the theoretical value,

And therefore a coefficient of discharge hade to be added to the equations, so that the become as follows;

Experiments are done in order to evaluate the exact values of "K" and "n" to be used for the calculation of discharge. From our experiment we measured the flow rate "Q" with the corresponding height "H", and a plot of log Q and log H was drawn in order to evaluate the coefficients where the slope represents "n" and the Y-Intercept represents log K as follow;

Apparatus: 1. 2. 3. 4.

A hydraulic bench. Rectangular and a V – notch. Stop watch. Vernier hook and point gauge.

Procedures: 1. The rectangular notch is clamped to the weir carrier by thumb nuts. 2. The vernier hook is calibrated so that its zero starts from the edge of the notch. 3. Several readings of time, volume and water level up stream is taken, with the flow rate increased each time. 4. Replace the rectangular notch by the V–notch and repeat the procedures 2 & 3 again.

Results:

Conclusions: 1. The general relation between "Q" and "H" was noticed experimentally to be empirical and direct, where an increase in water level at the upstream was accompanied with an increase in the rate of flow. Except for a single point at the rectangular notch which was considered as an experimental error. 2. The obtained values of the coefficient "n" was different from the theoretical values for both the rectangular notch and the V–notch where "n" obtained from the plots was as follows; Rectangular: n = 5/3 compared to the theoretical value n = 3/2. V–notch: n = 10/3 compared to the theoretical value n = 5/2. 3. The coefficient of discharge was represented by the value "K" as there where no dimensions available to evaluate Cd. 4. The value of the coefficient "K" for the rectangular notch (K=10.8) was much larger than it for the V – notch (K=0.04). That indicates the "Q" value is more sensitive to "H" for the rectangular weir than it for the V – notch.