Consider a fluid flowing in a conical section, as illustrated in Figure P5.75. The mass flow rate is the same going in (through point 1) as it is coming out (point 2), but the velocity changes because the area changes. They are related by

\[(ho V A)_{1}=(ho V A)_{2}\]

FIGURE P5.75 Flow in a cone.

where $ho$ is the fluid density (assumed to be constant here). Because the velocity changes, the transport of momentum will be different going in than going out, which results in a net force in the fluid.

(a) Derive an expression for the magnitude of this force associated with the change in momentum.

(b) Which direction will the force transmitted from the fluid to the cone act?

V, A r L X V2, A2