A steady, three-dimensional velocity field is given by V → = ( 0.657 + 1.73 x + 0.948 y + a z ) i → + ( 2.61 + c x + 1.91 y + b z ) j → + ( − 2.73 x − 3.66 y − 3.64 z ) k → Calculate constants a, b, and c such that the flow field is irrotational.
A steady, three-dimensional velocity field is given by V → = ( 0.657 + 1.73 x + 0.948 y + a z ) i → + ( 2.61 + c x + 1.91 y + b z ) j → + ( − 2.73 x − 3.66 y − 3.64 z ) k → Calculate constants a, b, and c such that the flow field is irrotational.
Solution Summary: The author explains the value of constants a, b and c. The flow field is irrotational. Write the expression for the two-dimensional velocity field in the vector form
A steady, three-dimensional velocity field is given by
V
→
=
(
0.657
+
1.73
x
+
0.948
y
+
a
z
)
i
→
+
(
2.61
+
c
x
+
1.91
y
+
b
z
)
j
→
+
(
−
2.73
x
−
3.66
y
−
3.64
z
)
k
→
Calculate constants a, b, and c such that the flow field is irrotational.
4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk ,
V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have
constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and
flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?
1. Stagnation Points
A steady incompressible three dimensional velocity field is given by:
V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k
Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s].
a) Determine coordinates of possible stagnation points in the flow.
b) Specify a region in the velocity flied containing at least one stagnation point.
c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal-
distance from your specified stagnation point.
Home Work (steady continuity equation at a point for incompressible
fluid flow:
1- The x component of velocity in a steady, incompressible flow field in the
xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find
the simplest y component of velocity for this flow field.
2- The velocity components for an incompressible steady flow field are u= (A
x* +z) and v=B (xy + yz). Determine the z component of velocity for
steady flow.
3- The x component of velocity for a flow field is given as u = Ax²y2 where
A = 0.3 ms and x and y are in meters. Determine the y component of
velocity for a steady incompressible flow. Assume incompressible steady
two dimension flow
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