Question

1. Falling Ball with Air Resistance (15 points) A round bal is dropped from a height for which air resistance is not negligible by the time the ball hits the ground A. On what dimensional parameters does the ball's impact speed depend? Define al symbols and give their dimensions B. Show at least three different ways that the impact speed may be made dimensionless C. On what dimensionless parameter(s) does the dimensionless speed depend? 2. Laminar Jet Toward Plate (15 points) When a laminar jet of fluid hits a flat wall under conditions of negligible friction, the velocity field near the center is as shown: k has dimension of time1 wall A. Show that the velocity satisfies the continuity equation for constant density. B. Derive an expression for the x component of the fluid acceleration, e for this velocity field. C. Derive an expression for the shear stress component Ty, for this velocity field D. Does any fluid pass through the plane defined by y -0? Yes or No E. Is the no-slip condition satisfied at the wall? Yes or No Why or why not? F. Derive an expression for the stream function of this flow

Answer 1

Solution R Velouty field is giveh by- A) Velouty componet in xdiyn is Comhnuity equ eton for Censtt density s Sy öy tence, the eloutyfield athifies comtinuity Velol

emponent in x-diyn is at 冰 S heh s Com |3υχ.tay hle know that Sheanstrain gate 2. So, sh eas. At ess componentてxy= 사4ateof shear てxy®o (D') Flow 18 2-D. leAn χahdy direction . it must be defined by y=0 C.,' in tha felane (B) ,. Tn the wall fruld focs in χ and in Y-direction

G) stream function is defind as as- koe - y dody Unx--Dunyt Inc "Х (on diffeh entiation) xy-ln