|Nov21-06, 03:37 PM||#1|
Derivation of Momentum Equation (Eulers Equation)
hey, i'm having difficulty understanding how Eulers Equation is derived... its because my grasp of calculus is preety bad.
Eulers equation is:
dp = -qVdV, where p is pressure, q is density and V is velocity. And thats clearly a differential equation. But i'd like to know how its derived. I know i have to start with newtons 2nd law:
my textbook says that
The force in the x direction acting on a fluid particle is
F = p dydz - (p + dp/dx dx) dydz (1)
Hence F = dp/dx dxdydz = force on fluid element due to pressure. (d)
This is where my confusion begins... I don't understand why the Force would be pressure multiplied by dydz and then minus pressure plus dp/dx multiplied by dydz. In other words i really dont understand whats going on with equation one, or how it becomes equation (2).
Can any1 help? I think once i understand this example i'll be able to work out others. Thanks.
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