Question

Describing Velocity Fields and Stream Lines A velocity field is given by, V= -yi + xj

a) Remark on the dimensionality, directionality and steadiness of the flow

b) Calculate the equation for the stream lines

c) Sketch (by hand) the streamlines through point x=2, y=0 and x=3, y=0

d) Describe in words what the flow pattern look like? Which of the following situations does the flow look like: Flow over a cylinder, flow into an acute corner, flow into 90 deg corner, flow against a wall, flow inside of a pipe, flow into a hole, flow over a step, and/or flow between two rotating cylinders? (note: there may be more than 1 correct descriptions). (Hint: No mass crosses a streamline.)

Answer 1

Given rewcity field Vi= gitu Step 1: N does not contain to variable it is steady + 24 - ди * 0 (-) 2 диди 0 in compresside 34 me How is too dimensional, implying no velocity and no va z- component of u ô v with z Shep 2: equation of Seamline du dy از زمان 2 -dy ? Greios oust auto - y2 = - x2 + c are circles x2 + y2 = Sheam lines Step 3: (=+2 y 2o at x=2 22 +02= c 1 & 4 circle with radices @ u= – 4 z o 3² +0²= ce ca £3 at n= 3, 430 u=- y =0 v2 = 33

U = -39 2 3 uz-2i 42 0:0 V-33 42d 4 0. UV-2010 V2 1002. 01 o k4,0) 12,0)3,0) 0,- +42-(2 Goo r ons ba i circled Sinseamlines, venticity vecto GORDO () (- ( +1) R = 2K be like flow The seems to aheamlines between two rotatin