SHARP-CRESTED WEIR LAB

BACKGROUND

Weirs measure flows in open channels

Bernoulli equation for ideal flow: (q = flow per unit width)


Energy Equation: (H_T = total head)

H_T = H + h_v = H + v²/2g






Flow Parameters

H_T = H + v²/2g

v = (2g(H_T - H))^0.5

v = (2g H (H_T/H - 1))^0.5
   = C (2g H)^0.5

Flow  Q = vA = C (2g H)^0.5 A




Sharp-Crested Weirs



Weirs may be broad-crested or sharp-crested

In CE 135, we use sharp-crested weirs


Rectangular: A = L H

V-notch: A = H^2.5 tan(θ/2)



Weir Equations

Q = vA

Rectangular Weir: Q = C (2gH)^0.5 L H
    C= arbitrary constant
Q = C (2g)^0.5 L H^1.5
       = C L H^1.5 or C H^1.5



V-notch Weir: Q = C (2g H)^0.5 H² tan(θ/2)
      = C H^2.5 tan(θ/2) or C H^2.5

    For θ = 90° V-notch, C ≈ 2.5, so approximately
Q = 2.5 H^2.5

FOR OUR EQUIPMENT

Rectangular weir has
L = b, where b is channel width

Thus, Q = C  b H^1.5


V-notch weir has

Q = α H^β tan (θ/2)


Our θ = 90°, so our value should be near

Q = 2.5 H^2.5




Flow Over Sharp-Crested Weir




 








V-notch or Triangular Weir

EXPERIMENTAL SET-UP

Calibrate Two Weirs

Tap 1 (before weir)
Manometer & point gage
Seeking height above weir

Run full range of flow rates

Profile In Rectangular Channel With Weir



Taps 1-3 before weir; tap 5, 6 & 7 after weir
Skip manometer tap 4 (under weir)

Two levels between taps 4 & 6
Over-flow of weir not in manometer taps
Point gage can hit both areas
(Sketch the pattern; points vary too much to just use data points)

Supercritical flow after weir

Closs off air vent & sketch new surface pattern

Weir In Half-Meter Flume In CE Lab




Force On Weir

Taps A-F
Water height above weir top


Direct Measurement:
F = Σγb(z_w-z₀+y_ti)Δy_i

Hydrostatic Force:
F = γb((z_w-z₀)²-((z_w-z₀+y_w)²)/2