Frcf= reactive centrifugal force...Frcf= -mv2/R

[Aeronautic Freek]

Pressure gradient normal to the local flow direction balance the centrifugal force associated with the curvature of flow..

Which centrifugal force inertial or "reactive" centrifugal force?

 

[A.T.]

Pressure gradient normal to the local flow direction balance the centrifugal force associated with the curvature of flow..

Which centrifugal force inertial or "reactive" centrifugal force?
View attachment 264265

There is no centrifugal force in your diagram.

 

[Aeronautic Freek]

There is no centrifugal force in your diagram.

That tell Doug Mclean who write this in his book...

 

[A.T.]

That tell Doug Mclean who write this in his book...

He didn't ask about the centrifugal force, you did.

 

[Aeronautic Freek]

He didn't ask about the centrifugal force, you did.

this is text from his book:
"Pressure gradient normal to the local flow direction balance the centrifugal force associated with the curvature of flow.. "

 

[A.T.]

this is text from his book:
"Pressure gradient normal to the local flow direction balance the centrifugal force associated with the curvature of flow.. "

The diagram apparently shows the inertial frame where there is no inertial centrifugal force on the fluid piece. The text seems to talk about a rotating frame where the centripetal net pressure force is balanced by an inertial centrifugal force.

 

[Aeronautic Freek]

The diagram apparently shows the inertial frame where there is no inertial centrifugal force on the fluid piece. The text seems to talk about a rotating frame where the centripetal net pressure force is balanced by an inertial centrifugal force.

yes but you said that inertial centrifugal force is not pair(balance) to centripetal force

 

[A.T.]

yes but you said that inertial centrifugal force is not pair(balance) to centripetal force

You are confusing Newtons 3rd Law pair with force balance in Newtons 2nd Law.

 

[Dale]

yes but you said that inertial centrifugal force is not pair(balance) to centripetal force

Third law pairs always act on different objects so they never balance each other. “Pair” relates to the third law and “balance” relates to the second law, so “pair(balance)” is kind of a contradiction.

 

[Chestermiller]

From the non-inertial frame of reference of an observer moving with the parcel of fluid, the centrifugal force is directed to the outside of the arc, and the force balance reads: $$P_{outside}A-P_{inside}A-F_c=0$$where $$F_c=m\frac{v^2}{R}$$with R representing the radius of curvature of the arc.

 

[Aeronautic Freek]

From the non-inertial frame of reference of an observer moving with the parcel of fluid, the centrifugal force is directed to the outside of the arc, and the force balance reads: PoutsideA−PinsideA−Fc=0where Fc=mv2Rwith R representing the radius of curvature of the arc.

Thanks.
How you would write equation for inertial frame?

(Pout - Pin) x A = Frcf ?

Frcf= "reactive centrifugal force"...Frcf=mv2/R

 

[A.T.]

Thanks.
How you would write equation for inertial frame?

(Pout - Pin) x A = Frcf ?

Frcf= "reactive centrifugal force"...Frcf=mv2/R

The 2nd Law equation for the parcel of fluid in the inertial frame would be:

(Pout - Pin) x A = Fcp

Fcp= "net centripetal force"...Fcp=mv2/R

The equation for Frcf that the parcel exerts on the neighboring parcels would be:

Frcf = -Fcp