1. Plot the discharge relationship for each device in Excel and determine the equation using a “power” type trendline.
2. Determine k and n values for each device from the trendline.
3. Re-calculate k using least-squares, by setting n = 0.5 (use Solver to minimise total error by changing the value of k)
4. Using the two values of k (from trendline and Solver), derive the value of C_d from the discharge equation for each device as shown below. Approximate expected values of C_d are also provided below for comparison with your results.
5. Comment on the results, and in particular how the results compared to expected values for C_d.

Supporting Information

For each device, you will need to look at the discharge equation (see equations for each device, listed below) in the form Q = khⁿ and then, using the “k” values obtained from the procedure on the left, rearrange the discharge equation to solve for C_d.

Bend meter, (C_d ~ 0.60 for comparison with experimental value)

where A is the cross-sectional area of the pipe (use nominal diameter given in the Apparatus section) and H is the difference in pressure head measured on the inside and outside of the bend.

Venturi meter, (Cd ~ 0.97 for comparison with experimental value)

where A₁ is the upstream cross-sectional area of the pipe (use nominal diameter given in the Apparatus section), H is the difference in pressure head measured on the inside and outside of the bend, D₁ is the upstream pipe diameter and D2 is the diameter in the throat (see Apparatus section).

Pitot tube meter (Cd ~ 0.99 for comparison with experimental value)

where A is the cross-sectional area of the pipe (use nominal diameter given in the Apparatus section) and H is the difference between the stagnation pressure and the static pressure.

Orifice meter (Cd ~ 0.66 for comparison with experimental value). Discharge equation identical to Venturi

Triangular weir (Cd ~ 0.6 for comparison with experimental value)

where θ is the weir angle and H is the height of water above the crest.