Hydraulic Jump Calculator, Formula, Calculation with Example

Hydraulic Jump Calculator:

Enter the Gravitational acceleration (g) in 9.80665m/s², Channel width (B) in meters (m), Discharge (Q) in cubic meters, Upstream depth (y₁) in meters(m), Upstream velocity (v₁) in m/s, Downstream depth (y₂) in m, Downstream velocity (v₂) in m/s, Head loss (ΔE) in m,  Jump length (L) in m, Jump height (h) in m, and you get the Jump efficiency in % .

Hydraulic Jump Calculator

Hydraulic Jump Properties:

Hydraulic jump properties is Froude number F1 is equal to the downstream velocity V1(m/s) in meter per second and divided by the root of the gravitational force g(m/s2) in meter per second2 and multiply the  downstream depth y1(m) in meter.Hence the Hydraulic jump formula can be written as

F1 = V1(m/s) /√ g(m/s2) * y1(m))

Derivation:

Froude number formula:

F1 = V1(m/s) /√ g(m/s2) * y1(m))

Depth ratio formula

Y2 / y1 =0.5 *[√(1+8 *Fr12)-1

Head loss formula

ΔE =(y2 – Y1)3 / (4 *Y1 *Y2)

Hydraulic jump height formula:

L=220 *y1 *tan h[(fr1 -1) /22

Hydraulic jump height formula:

H= y2 – y1

Jump efficiency equation:

En =[[√(8 *Fr12 +1)]3 -4 *Fr12 +1] /[ 8*Fr12(2+Fr12)] *100 %

F1 = upstream fraud number

V1 = upstream velocity in m/s

G=  gravitational acceleration in m/s2

Y1 = upstream depth in m

Y2/ y1 = depth ratio

ΔE = head loss

Y2 = downstream depth

L= hydraulic jump

H= hydraulic height

En =  jump efficiency

Example:1

Calculate the Y1 =20m, and v1=18 m/s .Find the Hydraulic jump value?

Answer:

F1 = V1 /√ g * y1)

F1 =18/√(9.8 *20)

F1 =1.28571425

Y2 / y1 =0.5 *[√(1+8 *Fr12)-1

Y2 / y1 =0.5 *[√(1+8 *1.285715)2-1]

Depth ration (y2/y1) =1.38576839

ΔE =(y2 – Y1)3 / (4 *Y1 *Y2)

ΔE =(27.71536794 -20)3 / (4*20 *27.71536794)

=0.2071377 m

L=220 *y1 *tan h[(fr1 -1) /22

L=220 *20 tan h [(1.28571425-1)/22]

L=57.1396 m

H= y2 – y1

H =27.7153679 -20

H=7.7153679 m

En =[[√(8 *Fr12 +1)]3 -4 *Fr12 +1] /[ 8*Fr12(2+Fr12)] *100 %

En =[[√(8 *1.285714852 +1)]3 -4 *(1.285714282 +1) /(8*1.28571428572) *(2+1.2857142857)2 *100%

Jump efficiency En =99.432974 %

Jump type =undular jump

Example:2

Calculate the y2=15m,and v2=13 m/s.Find the Froude number value?

Answer:

Y2 =15m

V2=13 m/s

G=9.8 m/s2

F1 = V1 /√ g * y1)

F1 =13 /√(9.8 *15 )

F –ration F2 =1.072221928

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