Experiment 4 - Flow Measurement with a V-Notch Weir

Object

To determine the relationship between the depth of water flowing over the weir and the discharge through the weir.

Apparatus

The following apparatus is required for this experiment:

  1. The weir as depicted in Figure 4.1.
  2. Set of calibrated weights (2.5 kg and 5.0 kg).
  3. Stop watch.


Figure 4.1.

Theory

The generally accepted formula for flow over a V-notch weir is:

Q = ( 8 ÷ 15 ) Cd ( 2 g ) 0.5 tan ( ß ÷ 2 ) h 2.5

where

Q = rate of discharge,
C d = coefficient of discharge,
ß = angle of the vee notch ( in this case 30 ° ),
g = acceleration due to gravity, and
h = head or height of water flowing through the vee notch.

Experimental Procedure

The procedure outlined below is to be followed for this experiment:

  1. Start with no weights on the hanger.
  2. Close valve A.
  3. Open valve B (ie. let the water out of the tank).
  4. Start pump.
  5. Open valve A so that water level rises to lower tip of weir.
  6. Set hook gauge at this level.
  7. Continue opening valve A until some head h is optained.
  8. To obtain the flow rate:
    1. Close valve B (ie. close outlet of weigh tank).
    2. The weighing beam will rise form the lower position to the upper stop.
    3. At the instant that the beam is in the horizontal position start the timer. Then immediately place the selected mass(es) on the weigh hanger.
    4. The beam will start to rise again. When the beam is in the horizontal position stop the timer and record the time interval, the mass on the hanger and the head of water passing through the vee notch.
    5. Open valve B (ie. let water out of weigh tank).
    6. Important - Remove masses before returning beam to its lower weighing position to avoid straining lever mechanism.
  9. Repeat step (7) to (8) for varous values of h.

Note: Depth of water upstream of the weir is measured by a hook gauge incorporated in the apparatus. Once water is flowing over the weir, it takes a long time for this depth to return to zero. Therefore, be sure to zero the hook gauge before you start the apparatus and be careful not to lose this zero point during your work. This procedure will save you considerable time.

Report

Compute the coefficient of discharge, Cd for the weir. Discuss your results.

Hint: Plot Q versus h on log-log paper. Compare the slope of the line with 2.5 and C d can be determined from the intercept of this line.

Table 4.1.