Select a research proposal topic that relates to electrical and electronics engineering and write a proposal report taking into
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Answer:
δu/δx+δu/δy = 6x-6x =0
9r^2
Explanation:
The flow is obviously two-dimensional, since the stream function depends only on the x and y coordinate. We can find the x and y velocity components by using the following relations:
u =δψ/δy = 3x^2-3y^2
v =-δψ/δx = -6xy
Now, since:
δu/δx+δu/δy = 6x-6x =0
we conclude that this flow satisfies the continuity equation for a 2D incompressible flow. Therefore, the flow is indeed a two-dimensional incompressible one.
The magnitude of velocity is given by:
|V| = u^2+v^2
=(3x^2-3y^2)^2+(-6xy)^2
=9x^4+18x^2y^2+9y^2
=(3x^2+3y^2)^2
=9r^2
where r is the distance from the origin of the coordinates, and we have used that r^2 = x^2 + y^2.
The streamline ψ = 2 is given by the following equation:
3x^2y — y^3 = 2,
which is most easily plotted by solving it for x:
x =±√2-y^3/y
Plot of the streamline is given in the graph below.
Explanation for the plot: the two x(y) functions (with minus and plus signs) given in the equation above were plotted as functions of y, after which the graph was rotated to obtain a standard coordinate diagram. The "+" and "-" parts are given in different colors, but keep in mind that these are actually "parts" of the same streamline.
Answer:
L= 312.75 mm
Explanation:
given data
elastic modulus E = 106 GPa
cross-sectional diameter d = 3.9 mm
tensile load F = 1660 N
maximum allowable elongation ΔL = 0.41 mm
to find out
maximum length of the specimen before deformation
solution
we will apply here allowable elongation equation that is express as
ΔL = ....................1
put here value and we get L
L =
solve it we get
L = 0.312752 m
L= 312.75 mm