Overflow coefficient

The discharge coefficient is a μ in hydraulic common dimensionless coefficient for calculating the amount of water during storage of a body of water by a fixed weir or a movable closure member coat (in response to the overflow height ). ${\ displaystyle h}$

use

The weir flow ( volume flow ) with the SI unit is determined according to the mathematical relationship often referred to as the Poleni formula: ${\ displaystyle Q}$ ${\ displaystyle \ mathrm {m ^ {3} / s}}$

{\ displaystyle {\ begin {aligned} Q & = {\ frac {2} {3}} \ cdot \ mu \ cdot {\ sqrt {2 \ cdot g}} \ cdot B \ cdot h ^ {3/2} \ \ & = {\ frac {2} {3}} \ cdot \ mu \ cdot {\ sqrt {2 \ cdot g}} \ cdot B \ cdot {\ sqrt {h ^ {3}}} \ end {aligned} }}

With

Acceleration due to gravity (= at the surface of the earth)

{\ displaystyle g}

{\ displaystyle 9 {,} 81 \, \ mathrm {m / s ^ {2}}}

Width of the raid

{\ displaystyle B}

Overflow height ( measured at least away from the overflow edge in the direction of the headwater , better further). ${\ displaystyle h}$ ${\ displaystyle 3h}$

Because the flow increases disproportionately with the overflow height, overflows are suitable structures for flood or emergency relief .

Conversely, the spill height increases only disproportionately with increasing spill volume:

{\ displaystyle {\ begin {aligned} \ Leftrightarrow h & = \ left ({\ frac {3} {2}} \ cdot {\ frac {Q} {\ mu \ cdot {\ sqrt {2 \ cdot g}} \ cdot B}} \ right) ^ {2/3} \\ & = {\ sqrt [{3}] {\ left ({\ frac {3} {2}} \ cdot {\ frac {Q} {\ mu \ cdot {\ sqrt {2 \ cdot g}} \ cdot B}} \ right) ^ {2}}} \ end {aligned}}}

This is why raids are ideal for regulating the water level when the outflows change .

values

The overflow coefficient is primarily a function of the transition shape and thus takes into account the shape of the beam deflection. For an initial pre-dimensioning , it is sufficient to assume the overflow coefficient for a weir or overflow structure that is straight in the floor plan according to the following information:

number	Training of the military crown	Overflow coefficient
1.	wide, sharp-edged, horizontal	0.49-0.51
2.	wide, well rounded edges, horizontal	0.50-0.55
3.	wide, completely rounded weir crown, reaches z. B. by a deflected storage flap	0.65-0.73
4th	sharp-edged, ventilated overflow jet	~ 0.64
5.	Round crown, vertical upstream and sloping downstream side	0.73-0.75
6th	Roof-shaped, rounded weir crown	0.75-0.79

Secondly, the overflow coefficient is also a function of the flow velocity and the amount of overflow water or the overflow height itself.

literature

Gerhard Bollrich, G. Preißler: Technical hydromechanics. 5th edition. Volume 1, Verlag für Bauwesen, 2000, ISBN 3-345-00744-4 .