Question

Consider the two dimensional Control Volume (CV) shown below in Fig. 1.1 for the special case of steady-state flow with v = 0 and a uniform pressure gradient vp = dp/axi = Ci everywhere C is a non-zero constant. These assumptions mean that both viscous shear stresses t = and compressive stresses due to pressure act on the fluid in the CV. You can also assume that there is no momentum source. - at itayº .. (x + 8x,y + 8y) P (x,y). - Xu Figure 1.1 Two Dimensional Control Volume Derive the x-momentum equation and simplify it as much as possible. You must define all terms used.

Answer 1

From the given data,

Hoswer * Consider two dimensional control volume (Cu). and * for the special case of steady-state flow wille van a uniform pressuve gradient vp = 3p) arts c. * Every where is a non-26x constant. * These assumptions mean that both viscous shear stresses тэр ч The compressive * stresses due to pressure act on the fluid in the cv. * Assume that there is no momentum Source. . + 2 by 3184 -.-.--. -(4+8x, y+84) S . AP+ voor YV . Two dimensional control volume

Steady stake flow v=0 . uniform pressure gradient op = p = ct ca constant viscous shear stresses La me sy - for x-momentum equation df = dfpt des - we know that . . dfp = pag an dr. Syaz dfs = (1+ ane by) Ex 82 -1 8482 df = dfg + dfs :: Pogg fx 2y 52 + ( a + 2 y by) 8x 8z -3 84 82 de 2 o y sy dr 82 st out ar - dn du 62 + ब dt 59