For a flow in the xy plane, the x component of velocity is given by u = Ax2y2, where A = 0.4 m-3 · s-1, and x and y are measured
in meters. (a) Find a possible y component for steady, incompressible flow. (b) Is it also valid for unsteady, incompressible flow? (c) How many possible y components are there? (d) Determine the equation of the streamline for the simplest y component of velocity (use C as constant).
1 answer:
Answer: v=(-2/3)*(A*x*y³)
The equation is not valid for the unsteady flow, as there is no dependence upon time neither on x or y component of the velocity,
The corresponding stream function:-
v(x,y)= (1/3)(A*x²*y³)
Coordinates through the streamline:- (1,4) and (2,4)
y(x) = Cx^(-2/3)
Explanation:
Use continuity equation:-
Integrate V to obtain to obtain:-
v= -2/3*A*x*y^3
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do= 61 cm
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