In deriving Bernoulli's equation , we equated the workdone on the fluid in the tube to its change in the potential and kinetic energy (a) How does the pressure change as the fluid moves along the tube if dissipative forces are present ? (b) Do the dissipative forces becomes more important as the fluid velocity increase? Discuss qualitatively.

Explanation

(a) When dissipative forces are present some amount of energy of the fluid is lost as it flows along the tube. While deriving Bernouli.s theorem we assume that the fluid is incompressible, thus the kinetic energy depends only on the cross sectional area of the pipe, so it does not get affected. Similarly, the potential energy being dependent on the height does not get affected. Hence, it is clear that the pressure energy is used to do work against the dissipative force. Therefore, the pressure drop is more as the fluid passes through the tube.
(b) In a fluid, the viscous forces are the dissipative forces present. For a viscous fluid, the drag force is given by `F=-eta A=(dv)/(dx)`
For a particular level, if the value of v increases, `(dv)/(dx)` obviously increases and hence the magnitude of the drag force increases. Hence it can be said that the dissipative forces become more important with increasing the fluid velocity.