FLUID MECHANICS - Review Summary of (some) Fluids Concepts Learned in 3015C Properties of Interest: Density, ; Temperature, T; Pressure, p (All properties can be a function of space and time (x,y,z,t) VELOCITY - V (x,y,z,t) Probably the most important one from a fluid mechanics perspective. Viscosity – Dynamic Viscosity,  (N.sec/m2); Kinematic Viscosity,  (m2/sec) Pressure Behavior (for static conditions) Pascal’s law: for a fluid at rest, I.e. under static conditions pressure acts uniformly in all directions. It also always perpendicular to the surface. Pressure variation: For a continuous fluid at rest the pressure varies according to: dp/dz = - g where z is the vertical direction, opposite to gravity Rigid Body Motion The ratio of linear (or angular) acceleration to the gravitational acceleration, determines the shape of the free surface. Buoyancy: The buoyancy force on a submerged object is equal to the weight of the fluid displaced by the object. (Applies for fully or partially submerged objects of all shapes)

Summary of (some) Fluids Concepts Learned in 3015C (cont’d) Boundary Layers: A region very close to solid surfaces where viscous effects are important A region very close to solid surfaces where velocity gradients are significant. Boundary layers can be Laminar or Turbulent Determined by the Reynolds Number Fundamental Equations of Motion: Conservation of Mass (continuity): Conservation of Momentum - If viscosity is neglected: Euler’s Equation OR

Summary of (some) Fluids Concepts Learned in 3015C (cont’d) Conservation of Momentum - If viscosity is neglected: Euler’s Equation Integrate Euler’s equation along a streamline to obtain Bernoulli’s Equation It is only valid for : incompressible fluids, steady flow along a streamline, no energy loss due to friction, no heat transfer Conservation of Energy - If energy is added, removed or lost via pumps turbines, friction, etc.then we use the energy equation or Extended Bernoulli’s Equation: Flow work + kinetic energy + potential energy = constant Where hA , hE is work done by or on the systems, e.g turbines, pumps, etc. and hL is Frictional Head Loss where