Derive the momentum and energy equation for unsteady quasi one dimensional flow. Express these in terms of non dimensional variables and suggest a method for its numerical solution
Derive the momentum and energy equation for unsteady quasi one dimensional flow. Express these in terms...
4. Obtain the momentum and energy integral equations for the unsteady two-dimensional laminar boundary layer equations (Ref: Problem 6.3, Convective Heat Transfer, Burmeister)
Momentum Theory Use one-dimensional conservation of momentum together with conservation of mass (continuity) and energy (Bernoulli’s equation = mechanical energy) to derive the power an ideal, frictionless wind turbine with an infinite number of blades, uniform thrust over the rotor area and a non-rotating wake can extract from the wind. Formulate the derivation in terms of the fractional decrease in wind velocity between the velocity far upstream and at the turbine rotor, ? = (? − ?)/?, also called “axial...
1. Consider the flow of a biological fluid to be described by the general dimensional version of the Navier-Stokes equation, ρ ir + (d' . V*)ύ.--V.P. + μν+2 " + ρ9-The stars indicate dimensional variables. Dimensional parameters, eg. ρ, g, etc., are un-starred. The characteristic velocity scale is V, and the characteristic length scale is L. The pressure scale is not apparent, but let's consider a few possible choices อย์" b. Non-dimensionalize the Navier-Stokes equation to determine a pressure scale...
Determine the equation of the momentum of a particle of mass m and kinetic energy KE. Express your answer in terms of the variables KE, m and c.
Determine the equation of the momentum of a particle of mass m and kinetic energy KE. Express your answer in terms of the variables KE, m and c. (KE/c) +mc is incorrect p=
Using the relativistic relationship between momentum and energy: a) Derive an expression for the wavelength of a particle with mass m in terms of its total energy. b) Compare this result to the expression for the wavelength of a photon in terms of energy and show that as m → 0, the expressions are equivalent.
Using the Energy Integral Equation (EIE), derive an expression for the average Nusselt number (in terms of Reynolds and Prandtl numbers) for laminar flow of a fluid over a surface with a free stream velocity of U. (which is a constant). Assume the fluid velocity in the momentum boundary layer is the same as the free stream velocity and (T-Tw)/(To-Tw)=(y/St), where T is the fluid temperature field in the thermal boundary layer, To is the free stream temperature, Twis the...
2. Use the scale analysis to derive momentum equation and energy equation of boundary layer under an external forced convection, and then determine the order pf magnitude of the ratio of thermal boundary layer thickness to hydrodynamic boundary layer thickness
roblem you will derive an equation for the QG streamfunction strophic secondary circulation. You should assume constant f da and that the geostrophic flow is two-dimensional (y2); specifically 6.4. In this ageostrophic seco an -Ue( t) only andsg(y.t) only. (a) Starting with geostrophic and hydrostatic balance, pof 0z show that the maintenance of thermal wind balance requires (b) Determine the left side of the result in (a) from the ug momentum equation. Dug fu Dtg Interpret the result physically energy...
1) Write down an equation for the conservation of momentum for two colliding objects in terms of masses, initial velocities, and final velocities. 2) Write down an equation for the total energy of two objects 3) Using these two equations, derive equations for the final velocity of each cart given that their initial velocities are both zero.