I am trying to solve a system of differential equations as follows:
L1 = 5.0;
L2 = 0.43;
d = 0.0056;
g = 9.8;
h1 = 5.0;
h2 = 0.43;
A1 = 0.00001;
A2 = 0.001;
p0 = 100000;
v0 = 0.001;
NDSolve[{P[t] -
1*1000*10*
L2 == (1000/(2*0.0056)*y[t]^2*
L2*(0.316*(1000*y[t]*0.0056/0.00089))^(-0.25)) +
500*01.7*y[t]^2, (1000*10*L1 -
P[t]) == (1000/(2*0.0056)*z[t]^2*
L1*(0.316*(1000*z[t]*0.0056/0.00089))^(-0.25)) +
500*01.7*z[t]^2, (y[t] - z[t])*0.0001 == v'[t],
P[t] == p0*v0/v[t],P[0]==100000,v[0]==0.001}, {P, v, y, z}, {t, 0, 1}]
Uppon ruuning the comand I get the following error message:"NDSolve::icfail: Unable to find initial conditions that satisfy the residual function within specified tolerances. Try giving initial conditions for both values and derivatives of the functions.". How can I make this work ?