Derive the equation of motion for isothermal systems.
Answers
The Equations of Change for Isothermal Systems flow in the system as a function of the imposed pressure difference. Neglect end effects and postulate that depends only on r and θ with the other velocity components zero. Fluid in Creeping flow in the region between two stationary concentric spheres. Fluid out 2e (a) Using the equation of continuity, show that toro)sin) where ur) is a function of r to be determined. (b) Write the θ component of the equation of motion for this system, assuming the flow to be slow enough that the term is negligible. Show that this gives 1 ag (3B.4-1) (c) Separate this into two equations (3B.4-2,3) where B is the separation constant, and solve the two equations to get 3, -9 2In cot(e/2) (91-92 R 41n cot(e/2)ド (3B.4-4) 11(r) = (3B.4-5) where g, and go2 are the values of the modified pressure at θ = ε and (d) Use the results above to get the mass rate of flow π-e, respectively. n@1-92)R3(1-r?ρ 12μ1n cotie/2) to = (3B.4-6)