damyarou

python, GMT などのプログラム

Hydraulic jump type energy dissipator

\begin{equation} v_1=0.9\cdot \sqrt{2\cdot g\cdot H} \end{equation}
\begin{equation} d_1=\cfrac{Q}{b\cdot v_1} \end{equation}
\begin{equation} F_1=\cfrac{v_1}{\sqrt{g\cdot d_1}} \end{equation}
\begin{equation} \cfrac{d_2}{d_1}=\cfrac{1}{2}\cdot \left(\sqrt{1+8\cdot F_1{}^2}-1\right) \end{equation}
\begin{equation} \cfrac{W}{d_1}=\cfrac{(1+2\cdot F_1{}^2)\cdot \sqrt{1+8\cdot F_1{}^2}-1-5\cdot F_1{}^2} {1+4\cdot F_1{}^2-\sqrt{1+8\cdot F_1{}^2}} -\left(\cfrac{\sqrt{g}}{C}\cdot F_1\right)^{2/3} \end{equation}
\begin{equation} L=4.5\cdot d_2 \end{equation}
\begin{align} & Q & & \text{discharge}\\ & b & & \text{width of apron}\\ & H & & \text{height from apron level to flood water level of reservoir}\\ & F_1 & & \text{Froude number at starting point of jump}\\ & v_1 & & \text{velocity at starting point of jump}\\ & d_1 & & \text{water depth at staring point of jump}\\ & d_2 & & \text{water depth at end point of jump}\\ & W & & \text{height of end sill}\\ & C & & \text{discharge coefficient of end sill}\\ & L & & \text{length of energy dissipator}\\ & g & & \text{gravity acceleration} \end{align} 
import numpy as np

def main():
    g=9.8
    q=42.0
    h0=554.1-321.0
    v1=26.5
    b=4.0

    d1=np.round(q/b/v1,decimals=3)
    fr=np.round(v1/np.sqrt(g*d1),decimals=3)
    d1d2=np.round(1/2*(np.sqrt(1+8*fr**2)-1),decimals=3)
    d2=np.round(d1*d1d2,decimals=3)
    print('v1=',v1)
    print('d1=',d1)
    print('Fr=',fr)
    print('d1d2=',d1d2)
    print('d2=',d2)

    c=1.704
    c1=(1+2*fr**2)*np.sqrt(1+8*fr**2)-1-5*fr**2
    c2=1+4*fr**2-np.sqrt(1+8*fr**2)
    cc=np.round(c1/c2-(np.sqrt(g)/c*fr)**(2/3),decimals=3)
    ww=np.round(d1*cc,decimals=3)
    print('cc=',cc)
    print('W=',ww)
    print('L=',4.5*d2)


#==============
# Execution
#==============
if __name__ == '__main__': main()

Calculation results are shown below.

v1= 26.5
d1= 0.396
Fr= 13.452
d1d2= 18.531
d2= 7.338
cc= 10.31
W= 4.083
L= 33.021

Thank you.