Question

Is there any reason for why a V-notch weir equation for flow rate will give much different values than the measured flow rate values in an experiment? The professor says this is intentional, and to find the reason why this is.

This is the V-notch equation mentioned:

Q=(8/15)(Cd)sqrt(2g)tan(theta/2) * H^2.5

The weir used had an angle of 60 degrees and the given discharge coefficient was 0.5767.

It should also be mentioned that using a power regression method on the measured values gave an accurate value for the exponent but a coefficient value nearly twice the coefficient value of the one in the V-notch equation.

Answer 1

The discharge over a triangular notch or weir is proportional to H^5/2, where H is the height of liquid surface above the sill of the notch or weir. As such the accurate measurement of head H is quite essential in order to obtain an accurate value of the discharge over the notch or weir. However, if an error is introduced in the measurement of the head it will affect the computed discharge.

Triangular Notch or Weir :
The discharge over a triangular notch or weir is given by,

where

Differentiating Q, we get:

Taking the ratio dQ/Q

  

  

shows that an error or 1% in measuring H will produce 2·5% error in discharge over a triangular notch or weir.

Also relatively large head required, particularly for free flow conditions.The upstream pool must be maintained clean of sediment and kept free of weeds and trash, otherwise the calibration will shift and the measurement accuracy will be compromised.

In power or exponential regression, the function is a power (polynomial) equation of the form or an exponential function in the form

Here y is Q and x is H

The goal of regression analysis is to determine the values of parameters for a function that cause the function to best fit a set of data observations that you provide.For power functions, we again take the log of both sides but plot log y versus log x.  If the transformed points are linear, then we find the Least-squares regression line (LSRL) for log y versus log x and do the inverse transformation to obtain the power function.