This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: z and using the z component of Euler’s equation, we find ∂ p ∂ z = f I ( z ) = − ρ g cos α = ⇒ f ( z ) = C − ρ gz cos α 494 CHAPTER 5. CONSERVATION OF MASS AND MOMENTUM where C is a constant. Thus, the pressure throughout the fluid in the car is p ( x, y, z ) = C − ρ gz cos α On the free surface, p = p a . Also, at x = 0 , inspection of Figure 5.13 shows that z = h , wherefore C = p a + ρ gh cos α Therefore, the pressure at any point in the fluid is p ( x, y, z ) = p a + ρ g ( h − z ) cos α On the free surface, p = p a . Thus, the equation of the free surface is p a = p a + ρ g ( h − z ) cos α = ⇒ z = h This means the free surface is parallel to the inclined plane, so that β = α...
View
Full Document
 '06
 Phares
 Acceleration, Force, Euclidean vector, Leonhard Euler, Euler characteristic

Click to edit the document details