If u and v are the components of velocity in the x and y directions of...
Solution:
Given,
u - ax + by
v = cx + dy
To find: Condition to be satisfied
We know that,
Continuity equation:
∂u/∂x + ∂v/∂y = 0
Substituting the given values, we get,
∂/∂x (u - ax + by) + ∂/∂y (cx + dy) = 0
Simplifying, we get,
-b + c = 0
Also,
Irrotational flow:
∂v/∂x - ∂u/∂y = 0
Substituting the given values, we get,
∂/∂x (cx + dy) - ∂/∂y (u - ax + by) = 0
Simplifying, we get,
a + d = 0
Therefore, the condition to be satisfied is
a + d = 0 or a = -d
If u and v are the components of velocity in the x and y directions of...
By substituting all the given conditions in the below relation, du/dx=-(dv/dy), Option: D; Satisfied this relation.
Given,
U= ax+by, V= CX+dy, substitute condition D, from the given options, i.e., a+d=0, in U & V we will get
U = ax+by
V = cx-ay
du/dx=-(dv/dy)
a=-a
Hence Condition satisfied.