b = 1.9552 m²/s 2.0206 y = 1.1 m V? ---- 1.7308 m2/s 1.7978 y = 1.0 m x= 1.5 m x= 1.6 m

3.3 Verify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (u, 1.j + u;41.j-1 - u.; – 4j.j-1) (1,j – 41,j-1) 2 Ax Ay where u and v are the x and y components of velocity, respectively. 3.4 Repeat Prob. 3.3, for the following difference representation for the continuity equation: (4i+ 1,5 - Uj-1,) (u, j+1 - V,j-1) + 2 Ax 2 Ay

P3.5 Water at 20°C flows through a 5-in-diameter smooth pipe at a high Reynolds number, for which the velocity profile is approximated by u = U.(v/R)/8, where U, is the cen- terline velocity, R is the pipe radius, and y is the distance measured from the wall toward the centerline. If the cen- terline velocity is 25 ft/s, estimate the volume flow rate in gallons per minute.

Water flows through a two-dimensional narrowing wedgeat 9.96 gal/min per meter of width into the paper(Fig. P4.72). If this inward flow is purely radial, find anexpression, in SI units, for ( a ) the stream function and( b ) the velocity potential of the flow. Assume onedimensionalflow. The included angle of the wedge is 45 ° .