The velocity field of a two - dimentional, incompressible flow is given by

\(\vec{V}=2 \sinh x ̂{i}+v(x, y) ̂{j}\)

where î and ĵ denote the unit vector in x and y direction, respectively. If v(x,0) = cosh x, then (0, -1) is

Explanation:

The velocity field of a two-dimensional, incompressible flow is given by,

\(\vec{V}=2 \sinh x \hat{i}+V(x, y) \hat{j}\)

and V(x, 0) = coshx,

For an incompressible flow, ∇ . \(\vec{V}\)  = 0

⇒ \(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\)

= 2coshx + \(\frac{\partial v}{\partial y}\) = 0

⇒ \(\frac{\partial v}{\partial y}\) = -2coshx

⇒ \(\int \partial v=\int-2 \cosh x \cdot \partial y\)

V = -2y . coshx + f(x)

For, V(x, 0) = coshx

⇒ -2y × coshx + f(x) = coshx

⇒ f(x) = coshx (at x, 0)

⇒ V = -2 . y × coshx + coshx

V = (1 - 2y) × coshx

V(0, - 1) = [1 - {2 × (-1)}] × cosh(0) = 3