Bernoulli equation is really just conservation of energy. It says that the internal energy of the fluid plus the kinetic energy of a fluid plus the potential energy of the fluid is constant. Usually this takes the form of:
P1*A1+1/2*v12+rho*g*h1= P2*A2+1/2*v22+rho*g*h2
where P is the pressure, A is the cross sectional area, v is the velocity of the fluid, rho is the density of the fluid, g is gravity, h is the height of the fluid, and the sub scripts denote the different points of the fluid.This is a simplied version of the equation, assuming no extra energy being added or lost, and assuming constant fluid density and constant mass flow. These are sometimes good assumptions. For historical and practical reasons, this equation is often described in terms of head, or distance. This is because if you have constant pressure, cross sectional area, and velocity, and you divide out rho*g, you are just adding distances.
1 hectare = 100 acres = 10000 meters squared = .01 kilometers squared.
144 square inches = 1 square foot.
0 Fahrenheit = 459.67 Rankine. 0 celsius = 273.15 K.
Basic equation for vibrations: m*x''+c*x'+k*x=0 m=mass, c=damper, k=spring constant, x=x(t), w=angular frequncy in radians per second, t=time in seconds, phi=initial angle in radians.
Since this is a second order differential equation it will have one of three solutions.
Overdampened case when c>2*sqrt(m*k)
x(t)=a*e(-c*t)+b*e(-d*t)
Perfectly dampened case when c=2*sqrt(m*k):
x(t)=a*e(-m*t)+b*e(-m*t)*t
Underdampened case when c<2*sqrt(m*k):
x(t)=a*e(-m*t)*cos(w*t+phi)+b*e(-m*t)*sin(wt+phi)