Hydraulic Jump in Horizontal Rectangular Channel

Enter discharge, channel width, upstream depth. Compute downstream depth, Froude numbers, depth ratio, velocities, hydraulic jump length and energy loss.


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  Channel width, B: 
Discharge, Q: 
Upstream depth, Y1
Downstream depth, Y2
Depth ratio, Y2/Y1
Jump length, L: 
  Head loss, h: 
© 2014 LMNO Engineering, Upstream Froude, F1
Research, and Software, Ltd. Downstream Froude, F2
http://www.LMNOeng.com Upstream velocity, V1
Downstream velocity, V2

Hydraulic jump calculation units: cm=centimeter, ft=foot, gal=US gallon, hr=hour, m=meter, MGD=Million Gallons (US) per Day, min=minute, s=second.

Hydraulic jump photoHydraulic jump diagram

Photograph from Ohio University's Fluid Mechanics Laboratory. Athens, Ohio USA


Hydraulic Jump Equations

Equations for hydraulic jump in horizontal rectangular channel (Chaudhry, 1993; Chow, 1959):

Q = V1 Y1 B = V2 Y2 B      F1 = V1 / (g Y1)0.5      F2 = V2 / (g Y2)0.5

Y2/Y1 = 0.5 [(1+8F12 )0.5 - 1]      L = 220 Y1 tanh[(F1-1)/22]        h = (Y2-Y1)3 /( 4 Y1 Y2)

where (subscript 1 indicates upstream of jump; subscript 2 indicates downstream of jump):
B=Channel width (m), F=Froude number (dimension-less), g=acceleration due to gravity (9.8066 m/s2), h=Head loss (m), L=Length of jump (m), Q=Discharge (m3/s), tanh=Hyperbolic tangent trigonometric function, V=Velocity (m/s), Y=Water depth (m)

What is a Hydraulic Jump?

A hydraulic jump occurs when the upstream flow is supercritical (F>1). To have a jump, there must be a flow impediment downstream. The downstream impediment could be a weir, a bridge abutment, a dam, or simply channel friction. Water depth increases during a hydraulic jump and energy is dissipated as turbulence. Often, engineers will purposely install impediments in channels in order to force jumps to occur. Mixing of coagulant chemicals in water treatment plants is often aided by hydraulic jumps. Concrete blocks may be installed in a channel downstream of a spillway in order to force a jump to occur thereby reducing the velocity and energy of the water. Flow will go from supercritical (F>1) to subcritical (F<1) over a jump.

According to Chow (1959), a strong jump occurs when F1>9, a steady jump occurs when 4.5<F1<9, an oscillating jump occurs when 2.5<F1<4.5, a weak jump occurs when 1.7<F1<2.5, and an undular jump occurs when 1<F1<1.7. According to Chaudhry (1993), the best jumps occur when 4.5<F1<9.

"Need B>0."  Channel width must be a positive number.
"Need Q>0."  Discharge must be positive.
"Need Y1>0."  Upstream depth must be positive.
"Need F1 >1."  Upstream flow must be supercritical.

Chaudhry, M. H. 1993. Open Channel Flow. Prentice-Hall, Inc.

Chow, V. T. 1959. Open Channel Hydraulics. McGraw-Hill, Inc.

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