Fluid Flow Measurement with Weirs: Types, Formulas, and Applications, Slides of Hydraulics

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WEIRS

Fluid Flow Measurement

Weirs

• overflow structures that are built across an open channel to measure or control the flow of liquids. Classification of Weirs ➢ Rectangular ➢ Triangular ➢ Trapezoidal ➢ Circular ➢ Parabolic

Contracted weir – weirs having sides sharp-edged so that the nappe is contracted in width or having end contractions, either one end or two ends Suppressed weir (full-width weir) – weirs having its length L being equal to the width of the channel so that the nappe suffers no end contractions Nappe – the overflowing seam in the weir Crest of weir – the edge or top surface of a weir with which the flowing liquid comes in contact

Drop-down curve – the downward curvature of the liquid surface before the weir Head, H – the distance between the liquid surface and the crest of the weir, measured before the drop- down curve

𝑸 = 𝟐 𝟑 𝑪 𝟐𝒈𝑳 𝑯 + 𝒉 𝒗 𝟑 𝟐 (^) − 𝒉 𝒗 𝟑 𝟐

𝑸 = 𝑪 𝒘 𝑳 𝑯 + 𝒉 𝒗 𝟑 𝟐 (^) − 𝒉 𝒗 𝟑 𝟐 C w is the weir factor equal to 2 3 𝐶 2𝑔 𝑸 = 𝑪 𝒘 𝑳𝑯 ൗ 𝟑 𝟐 If the H/P ratio is sufficiently small, the velocity approach becomes very small the h v 3/ may be neglected

Standard Weirs

Standard Weir

The following specifications must be applied to standard rectangular weirs without end contractions: ➢The upstream face of the weir plate should be vertical and smooth ➢The crest edge shall be level, shall have a square upstream corner, and shall be narrow that the water will not touch it again after passing the upstream corner.

Standard Weir Factors (C

w

FRANCIS FORMULA

𝑪 𝒘 = 𝟏. 𝟖𝟒 𝟏 + 𝟎. 𝟐𝟔 𝑯 𝒅 𝟐 (SI Units) Based upon experiments on rectangular weirs from

1. 07 m ( 3. 5 ft) to 5. 18 m ( 17 ft) long under heads from 180 mm to 490 mm

Standard Weir Factors (C

w

𝑪 𝒘 = 𝟏. 𝟖𝟒 (SI Unit) 𝑪 𝒘 = 𝟑. 𝟑𝟑 (English Unit) For H/P < 0. 40 the following C w may be used:

Standard Weir Factors (C

w

BAZIN FORMULA

𝑪 𝒘 = 𝟎. 𝟓𝟓𝟏𝟖 𝟑. 𝟐𝟒𝟖 + 𝟎. 𝟎𝟐𝟏𝟔𝟏 𝑯 𝟏 + 𝟎. 𝟓𝟓 𝑯 𝒅 𝟐 (SI Units) For rectangular weirs of length from 0. 5 m to 2. 0 m under heads from 50 mm to 600 mm.

Contracted Rectangular Weir

Contracted Rectangular Weir

where: L’ = measure length of crest N = number of end contraction H = measured head

Triangular Weir (V-Notch)