Start with equation of state and substitute for temperature

Assignment Help Mechanical Engineering

Reference no: EM13708146

An important concept in using CFD code to solve the Navier-Stokes equations is that the variables set that are solved for are the ones appearing in the time derivative terms. These are called conservative variables. For a one-dimensional calorically perfect gas, derive the following:

(a) An expression for pressure, P, in terms of density and energy (HINT: start with the equation of state and substitute for temperature)

(b) Using (a), an expression for pressure in terms of the three conservative variables, (density), (density u), (density e0) (give these three things each a symbol if you like or just make sure they are clearly grouped together in your answer)

Reference no: EM13708146

Questions Cloud

A material has a strength coefficients : A material has a strength coefficients K = 100, 000 psi Assuming that a tensile-test specimen made from this material begins to neck at a true strain of 0.17, show that the ultimate tensile strength of this material is 62,400 psi.

How much energy in mev is produced from this event : In a particular fission event, a thermal neutron produces fission of a U-235 atom. For this particular event, the fission products Br-90 and Xe-143 are produced as well as 3 neutrons. How much energy in MeV is produced from this event?

Calculate the volumetric efficiency when the piston speed : A naturally-aspirated, direct-injection, four-stroke diesel engine has a total displacement volume of 10L, 125 mm bore and 16.3:1 compression ratio. The engine produces a maximum of 210 kW at 2100 RPM. Assuming that the intake air is at 45Â°C and 22...

Compute the energy equation flux of the gas : A specific point during the re-entry flight of the Space Shuttle has the following condition: Mach number of 15.93, static pressure of 20 Pa, and static temperature of 245 K. Assuming that air is a calorically perfect gas and that this condition is s..

Start with equation of state and substitute for temperature : An important concept in using CFD code to solve the Navier-Stokes equations is that the variables set that are solved for are the ones appearing in the time derivative terms. These are called conservative variables. An expression for pressure, P, in ..

Determine load that is necessary to produce such elongation : A cylindrical bar of a metal alloy of 1.5cm in diameter and 38cm in length is loaded in tension which produces an increase in length of 0.19cm. If its yield strength is 240 MPa, its tensile strength is 310 MPa and its elastic modulus is 110 GP, deter..

Derive the continuity equation from first principles : Derive the continuity equation from first principles using an infinitesimal control volume of rectangular shape and having dimensions (?x, ?y, ?z). Identify the net mass flow rate through each surface of this element as well as the rate at which the ..

Insulated piston-cylinder assembly containing a fluid : An insulated piston-cylinder assembly containing a fluid has a stirring device operated externally. The piston is frictionless, and the force holding it against the fluid is due to standard atmospheric pressure and a coil spring. The spring constant ..

An automobile engine consumes fuel at a rate : An automobile engine consumes fuel at a rate of 29 L/hr and delivers 60 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the efficiency of this engine, and draw a conceptual schematic of..

User Account

All Pages