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ANY MATHEMch ERRORS D\MENS‘OMAULH’ iNCoRREQT IN unﬁt: . uxbmc‘ 
UNIVERSITY OF CALIFORNIA, BERKELEY
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ME106 . Fluid Mechanics  NAME QEizELLlEES
lst Test, SOB Prof S. MOMS 1.(65) (a) Find the ﬂuid acceleration a for plane stagnation point ﬂow in which the velocity is given
by the expression V = cmi — cyj (the Constant c > 0).
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IN BLOCK LETTERS PRINT YOUR NAME ON THIS PAGE “9 1508—1 2. (65) The vector ﬁeld V : iécrf—Fvﬁ‘, 2367+ c212 {c > 0, constant)
stretched in the axial direction. For this ﬂow, the ﬂuid acceleration is 2 a= (ice * 3:)H (9‘1 e if? at ’1‘ WKQ Swag
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Air enters the gap between the discs with speed Vb through the supply tube of radius a, ﬂows radiain
and leaves as a free jet into the atmosphere Atmospheric pressure is pa. Within the gap, the Speed V
varies with distance r from the axis according to the rule v={ (You are not required to show that.) The pressure within the supply tube is unknown; it is not
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(c) Hence show that F is given by the expressionk m‘l‘ k.) H \O 93v can“: (9 1‘ 3.. Fan...) Via1N mammal? . a4 R Explain physically why, despite the presence of a stagnation point at O, the force is upwards if R > a. (2
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 Spring '08
 Morris
 Fluid Dynamics, Stagnation Point, stagnation point ﬂow, ﬂuid acceleration, SOB Prof S., MATHEMch ERRORS D\MENS‘OMAULH

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