Engineering
Chezy Open-Channel Velocity, Critical Depth (y_c) & Specific Energy
Compute Chezy velocity for uniform flow, then explore rectangular-channel critical depth, minimum specific energy and Froude number using explicit SI inputs.
Separate the uniform-flow and critical-flow calculations
The Chezy example uses V=C sqrt(Rh Sf), where Rh=area/wetted perimeter in metres and Sf is the dimensionless energy slope. C has SI units m^(1/2)/s. Bed slope equals energy slope only under the uniform-flow assumption; a flat bed alone does not imply zero flow.
The rectangular critical-flow example uses unit-width discharge q=Q/width in m²/s, gravity g in m/s² and actual depth y in metres. With hydrostatic pressure and velocity-head coefficient alpha=1, critical depth is (q²/g)^(1/3), and minimum specific energy is 1.5 times that depth.
The Chezy inputs and unit-discharge example are independent illustrations. This sheet does not solve a channel geometry that makes both cases consistent. It does not locate a hydraulic jump or compute a full water-surface profile.
For the rectangular case, Fr=q/(y sqrt(gy)) and specific energy E=y+q²/(2gy²). Classify positive flow using Fr; a tolerance of 1e-9 around 1 is a numerical display convention. Zero discharge is reported as no flow, not a finite positive critical depth.
Chezy velocity in D2
Use a coefficient appropriate to the units and resistance model. The zero energy-slope result is the model limit.
=IF(COUNT(B2:B4)<>3,"Enter numeric Chezy inputs",IF(OR(B2<=0,B3<=0,B4<0),"Require C>0, radius>0 and slope>=0",B2*SQRT(B3*B4)))Rectangular critical depth in D3
Keep the unrounded result to test Fr=1 at critical depth.
=IF(COUNT(B5:B6)<>2,"Enter numeric discharge and gravity",IF(OR(B5<0,B6<=0),"Require q>=0 and gravity>0",IF(B5=0,"No positive-flow critical depth",(B5^2/B6)^(1/3))))Minimum specific energy in D4
This is energy per unit weight relative to the channel bed, in metres, for the stated rectangular model.
=IF(ISNUMBER(D3),1.5*D3,D3)Froude number at depth B7, in D5
Try a depth above and below D3 to see the two flow regimes.
=IF(COUNT(B5:B7)<>3,"Enter numeric q, gravity and depth",IF(OR(B5<0,B6<=0,B7<=0),"Require q>=0, gravity>0 and depth>0",B5/(B7*SQRT(B6*B7))))Specific energy at depth B7, in D6
At the same positive q, this value reaches its minimum when B7 equals D3.
=IF(COUNT(B5:B7)<>3,"Enter numeric q, gravity and depth",IF(OR(B5<0,B6<=0,B7<=0),"Require q>=0, gravity>0 and depth>0",B7+B5^2/(2*B6*B7^2)))Regime label in D7
Uses the calculated Froude number, not the rounded display value.
=IF(NOT(ISNUMBER(D5)),D5,IF(B5=0,"No flow",IF(ABS(D5-1)<0.000000001,"Critical",IF(D5<1,"Subcritical","Supercritical"))))Try the example
Use the original values or change them to test your understanding.