Fluid Dynamics Issues - Assignment Example

FLUID DYNAMICS by Student’s name Code+ course name Professor’s name University name City, State Date Fluid Dynamics Question 1.1 Navier-Strokes Equations are equations that govern the flow of liquids and gases which when seen under the microscope, are seen to be continuous and also governs the heat flow through these fluids. These equations are time dependent and also consist of elements of momentum which is associated with conservation of mass equations, equations of energy conservation as well as equations that describe momentum conservation. The listed below are the Navier-Strokes Equations[Dra06]. a Instantaneous equation: b Momentum Equation: c Energy Equation: Linear momentum conservation equations are often used in the cases of both momentum and continuity equations. Linear momentum conservation equations, in this case, can be put in the form below. Where: j=momentum density at the point of the fluid considered to be continuous. F= flux associated with the momentum density. S= all the body forces per unit density. t= time. It is important to note that j and s have equal magnitudes N as the speed of the body increases. Question 1.2 Question 2.1 SI unit for density = kg/m3 SI unit for velocity = m/s SI unit for dynamic viscosity = kg/ms From the given equation we can derive the SI units of the dimension presented = kg/m3 x m/s x m2s2/kg2 = kg/s From the derived SI units, the dimension is Mass Flow Rate Question 2.2 Kolmogorov’s velocity, v = (ʋƐ0)1/4 Where ʋ = m2/s, and Ɛ0 = m2/s3 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