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Hydraulic Jump Analysis
Core Numerical Engine in Fortran 90 • 89 total downloads
hydraulic_jump.f90
! =========================================================================
! Source File: hydraulic_jump.f90
! =========================================================================
! ============================================================
! ThermoFluidCalc — Hydraulic Jump Calculator
! Solve for conjugate state y2, energy loss, jump length, etc.
! Supports: rectangular horizontal channel
! ============================================================
program hydraulic_jump
implicit none
real(8), parameter :: g = 9.81d0
real(8), parameter :: PI = 3.141592653589793d0
real(8), parameter :: RHO = 1000.0d0
real(8), parameter :: NU = 1.0d-6
real(8) :: y1, b, flow_val, y2
integer :: input_mode
real(8) :: V1, V2, Q, q_width, Fr1, Fr2, E1, E2, h_L, efficiency
real(8) :: h_j, L_j, P_loss, Re1, Re2
character(len=20) :: mode_name, regime1, regime2
character(len=60) :: jump_class, energy_diss_desc
! Read inputs
read(*,*) y1 ! Upstream depth [m]
read(*,*) b ! Channel width [m]
read(*,*) input_mode ! 1 = Given V1, 2 = Given Q, 3 = Given Fr1
read(*,*) flow_val ! Flow rate parameter value
! Validate geometry
if (y1 <= 0.0d0 .or. b <= 0.0d0) then
write(*,'(A)') "ERROR: Upstream depth y1 and width b must be positive."
stop
end if
! Compute flow state depending on input mode
select case (input_mode)
case (1)
mode_name = 'Upstream Velocity V1'
V1 = flow_val
Q = V1 * y1 * b
Fr1 = V1 / sqrt(g * y1)
case (2)
mode_name = 'Total Discharge Q'
Q = flow_val
V1 = Q / (y1 * b)
Fr1 = V1 / sqrt(g * y1)
case (3)
mode_name = 'Upstream Froude Fr1'
Fr1 = flow_val
V1 = Fr1 * sqrt(g * y1)
Q = V1 * y1 * b
case default
write(*,'(A)') "ERROR: Invalid input mode."
stop
end select
! Verify that the flow is supercritical (Fr1 > 1.0)
if (Fr1 <= 1.0d0) then
write(*,'(A,F10.4)') "ERROR: Upstream flow must be supercritical (Fr1 > 1.0). Current Fr1 = ", Fr1
stop
end if
! Compute downstream conjugate state
y2 = (y1 / 2.0d0) * (-1.0d0 + sqrt(1.0d0 + 8.0d0 * Fr1**2))
V2 = Q / (y2 * b)
Fr2 = V2 / sqrt(g * y2)
q_width = Q / b
! Specific Energy
E1 = y1 + V1**2 / (2.0d0 * g)
E2 = y2 + V2**2 / (2.0d0 * g)
h_L = E1 - E2
efficiency = (E2 / E1) * 100.0d0
h_j = y2 - y1
! Power dissipated
P_loss = RHO * g * Q * h_L / 1000.0d0 ! in kW
! Reynolds Numbers
Re1 = V1 * y1 / NU
Re2 = V2 * y2 / NU
! Jump length and classification
if (Fr1 <= 1.7d0) then
jump_class = 'Undular Jump'
energy_diss_desc = 'Very low energy dissipation (< 5%)'
L_j = 4.0d0 * y2
else if (Fr1 <= 2.5d0) then
jump_class = 'Weak Jump'
energy_diss_desc = 'Low energy dissipation (5% to 15%)'
L_j = 4.0d0 * y2 + (Fr1 - 1.7d0)/(2.5d0 - 1.7d0) * 1.0d0 * y2
else if (Fr1 <= 4.5d0) then
jump_class = 'Oscillating Jump'
energy_diss_desc = 'Moderate energy dissipation (15% to 45%)'
L_j = 5.0d0 * y2 + (Fr1 - 2.5d0)/(4.5d0 - 2.5d0) * 1.1d0 * y2
else if (Fr1 <= 9.0d0) then
jump_class = 'Steady Jump'
energy_diss_desc = 'High energy dissipation (45% to 70%)'
L_j = 6.1d0 * y2
else
jump_class = 'Strong Jump'
energy_diss_desc = 'Very high energy dissipation (> 70%)'
L_j = 6.1d0 * y2 - (Fr1 - 9.0d0)/(20.0d0 - 9.0d0) * 0.5d0 * y2
if (L_j < 5.6d0 * y2) L_j = 5.6d0 * y2
end if
! Regime descriptors
regime1 = 'Supercritical (Fr>1)'
if (Fr2 < 1.0d0) then
regime2 = 'Subcritical (Fr<1)'
else
regime2 = 'Critical (Fr=1)'
end if
! === OUTPUT ASCII REPORT ===
write(*,'(A)') '============================================================'
write(*,'(A)') ' HYDRAULIC JUMP CALCULATOR'
write(*,'(A)') '============================================================'
write(*,*)
write(*,'(A)') '--- INPUT CONFIGURATION ---'
write(*,'(A,F12.4,A)') ' Channel Width (b) = ', b, ' m'
write(*,'(A,A)') ' Input Selection Mode = ', trim(mode_name)
write(*,'(A,F12.4,A)') ' Upstream Depth (y1) = ', y1, ' m'
select case (input_mode)
case (1)
write(*,'(A,F12.4,A)') ' Upstream Velocity (V1) = ', V1, ' m/s'
case (2)
write(*,'(A,F12.4,A)') ' Total Discharge (Q) = ', Q, ' m3/s'
case (3)
write(*,'(A,F12.4)') ' Upstream Froude (Fr1) = ', Fr1
end select
write(*,*)
write(*,'(A)') '--- CONJUGATE STATE PROPERTIES ---'
write(*,'(A,F12.4,A)') ' Upstream Depth (y1) = ', y1, ' m'
write(*,'(A,F12.4,A)') ' Downstream Depth (y2) = ', y2, ' m'
write(*,'(A,F12.4,A)') ' Upstream Velocity (V1) = ', V1, ' m/s'
write(*,'(A,F12.4,A)') ' Downstream Velocity (V2)= ', V2, ' m/s'
write(*,'(A,F12.4)') ' Upstream Froude (Fr1) = ', Fr1
write(*,'(A,F12.4)') ' Downstream Froude (Fr2) = ', Fr2
write(*,'(A,A)') ' Upstream Flow Regime = ', trim(regime1)
write(*,'(A,A)') ' Downstream Flow Regime = ', trim(regime2)
write(*,'(A,F12.4,A)') ' Total Discharge (Q) = ', Q, ' m3/s'
write(*,'(A,F12.4,A)') ' Discharge per Width (q) = ', q_width, ' m2/s'
write(*,'(A,ES12.4)') ' Upstream Reynolds (Re1) = ', Re1
write(*,'(A,ES12.4)') ' Downstream Reynolds(Re2)= ', Re2
write(*,*)
write(*,'(A)') '--- JUMP HYDRAULICS & LOSSES ---'
write(*,'(A,F12.4,A)') ' Upstream Energy (E1) = ', E1, ' m'
write(*,'(A,F12.4,A)') ' Downstream Energy (E2) = ', E2, ' m'
write(*,'(A,F12.4,A)') ' Energy Head Loss (h_L) = ', h_L, ' m'
write(*,'(A,F12.2,A)') ' Jump Efficiency (E2/E1) = ', efficiency, ' %'
write(*,'(A,F12.4,A)') ' Jump Height (y2 - y1) = ', h_j, ' m'
write(*,'(A,F12.4,A)') ' Estimated Jump Length = ', L_j, ' m'
write(*,'(A,F12.4,A)') ' Power Dissipated = ', P_loss, ' kW'
write(*,*)
write(*,'(A)') '--- FLOW REGIME CLASSIFICATION ---'
write(*,'(A,A)') ' Jump Classification = ', trim(jump_class)
write(*,'(A,A)') ' Energy Dissipation = ', trim(energy_diss_desc)
write(*,*)
write(*,'(A)') '--- EQUATIONS USED ---'
write(*,'(A)') ' Conjugate Depth: y2 = (y1/2) * [-1 + sqrt(1 + 8*Fr1^2)]'
write(*,'(A)') ' Specific Energy: E = y + V^2 / (2g)'
write(*,'(A)') ' Head Loss: h_L = E1 - E2 = (y2 - y1)^3 / (4 * y1 * y2)'
write(*,'(A)') ' Power Dissipated: P = rho * g * Q * h_L'
write(*,'(A)') '============================================================'
end program hydraulic_jump
Solver Description
A hydraulic jump occurs when a rapid, supercritical open-channel flow ($Fr_1 > 1.0$) transitions abruptly to a slower, subcritical flow ($Fr_2 < 1.0$), dissipating mechanical energy. The relationship between upstream depth ($y_1$) and downstream depth ($y_2$) is given by the Belanger equation:
Key Numerical Methods & Architecture
- Input Redirection: Reads parameters sequentially from standard input (`stdin`) using Fortran sequential read (`read(*,*)`), ensuring modular integration.
- Modular Design: Formulated using pure mathematical routines, separation of equations from output formatting, and precise numerical solvers (e.g. bisection, Newton-Raphson).
- Standard Compliant: Written in clean, standards-compliant Fortran 90 to ensure cross-compiler compatibility.
🛠️ Local Compilation
To test this code on your machine, compile the source code file(s) using a standard Fortran compiler (e.g., `gfortran`).
Compilation Command:
gfortran -O3 hydraulic_jump.f90 -o hydraulic_jump_calc
Execution Command:
Execute the program by feeding the sample input file into the program using stdin redirection:
hydraulic_jump_calc < input.txt
📥 Downloads & Local Files
Preview of the required input file (input.txt):
! Initial water depth y1 [m]
0.3
! Channel width b [m]
2.0
! Flow input mode (1=Discharge Q [m3/s], 2=Froude Number Fr1)
1
! Flow parameter value
5.0
0.3
! Channel width b [m]
2.0
! Flow input mode (1=Discharge Q [m3/s], 2=Froude Number Fr1)
1
! Flow parameter value
5.0