Fluid Dynamics: Navier-Strokes Equations - Assignment Example

FLUID DYNAMICS by Student’s name Code+ course name Professor’s name University name City, State Date Fluid Dynamics 1.1 Navier-Strokes Equations- these are the equations that have been developed to govern the viscous heat conducting fluid. This is a vector equation that is derived from application of Newton's law to a fluid element. It also refers to momentum equation of which its supplement is mass conservation equation known as continuity equation/energy equation. The following equation takes refers to Navier-Strokes equation: a) Instantaneous equation: b) Momentum Equation: c) Energy Equation: Equations for the conservation of linear momentum are always used for both momentum and continuity equations and energy equations at times. It can be put in the following form (conservation form)[Soh12] j = momentum density at the point considered in a continuum F= flux associated with momentum density S= all the body forces per unit density. Both j and s have similar lengths N as the flow speed the body acceleration, 1.2 2.1 From the provided equation, we can derive the SI unit that will help us identify the dimension presented by it Where, = density, v = velocity, and µ = dynamic viscosity Density SI unit = kg/m3 Velocity SI unit = m/s Viscosity SI unit = kg/ms From the SI units of density, velocity and viscosity, we can derive the SI units using the following calculation = kg/m3 x m/s x m2s2/kg2 = kg/s The derived SI unit kg/s present Mass Flow Rate dimension 2.2 The Kolmogorov’s velocity (v) is presented by the following equation v = (ʋƐ0)1/4 Where ʋ = m2/s, and Ɛ0 = m2/s3 Ɛ0 is referred to as the rate of energy dissipation If E (k) represents the density of contributions to the kinetic energy per unit scalar wave number, irrespective of direction. Then, the energy in each k, can be found as follows: E (k) = v2Ƞf(kȠ), = k-5/3F(kȠ) At the inertial subrange I-1 Read More