Question #229400

Show that curl(curl→{v})=grad(div→{v})-V^{2}→{v},→{v} is any vector and if isolenoidal, then find curl (curl →{v)?

Expert's answer

The provided equation is :

curl(curl→{v})=grad(div→{v})-V^{2}→{v},→{v}

And to show that

In that equation, any is a vector:

= ˆr r sin θ ∂ ∂θ (aφ sin θ) − ∂ ∂φ(aθ) + θˆ r sin θ ∂ ∂φ(ar ) − ∂ ∂r (aφr sin θ) + φˆ r ∂ ∂r (aθr ) − ∂ ∂θ (ar )

And if isolenoidal,

To determine curl (curl →{v):

We can begin by summing the pair of the equation to obtain:

Then, together with the other pair as:

The curl equation for (curl →{v) therefore becomes:

Learn more about our help with Assignments: Chemical Engineering

## Comments

## Leave a comment