MECH 314 Notes 3, Spring 2014

MECH 314 Introduction to Fluid Mechanics February 19, 2009 American University of Beirut, Spring 2009 Handout # 3 Fluid Statics 1. (Lecture 1) In a static fluid shear stresses are zero. The only surface stress acting on a fluid element is pressures. The pressure acting at a point in a fluid is independent of the orientation of the plane on which it is acting. This a consequence of the fact that in the limit of a vanishing element size, body forces cannot balance surface forces, the normal stresses have to balance themselves. 2. (Lecture 1) Pressure force per unit volume acting at point in fluid is Fpressure = −∇p. 3. (Lecture 1) Momentnum equation for flow in the absence of viscous forces: Newton’s second law on a differential element dV : ρ Du Dt = −∇p + ρg 4. (Lecture 1) Conditions under which viscous forces vanish: (1) Hydrostatics: Flow at rest or at constant velocity. (2) Rigid body translation and rotation. (3) Inviscid flow (Bernoulli’s equation) 5. (Lecture 2) Hydrostatics: ∇p = ρg with g = −gˆz, then ∂p ∂x = 0 ∂p ∂y = 0 ∂p ∂z = −γ, where specific weight γ ≡ ρg. Analysis: Pressure is constant at all points in a given horizontal plane. The pressure increases with depth. Examples: (1) Static bodies of fluid in atmosphere: p(z) = pa − γz, with z pointing upwards from surface. (2) The mercury barometer. (3) Manometry; the simple manometer (will be covered in the homework.) (4) Hydrostatic pressure in ideal gases (will be covered in the homework.) (5) Hydrostatic forces on plane and curved surfaces. 6. (Lecture 3) Rigid body translation and rotation. 7. (Lecture 4) Buoyancy and stability (for floating and submerged bodies). Read: White Chapter 2 1