Does there need to be a difference in pressure for a fluid to accelerate?

[miaou5]

From some of the questions I'm encountering my text, it seems like the writers are implying that there always needs to be a difference in pressure for a fluid to accelerate (by this I mean a difference between the Pi and Pf values on either side of Bernoulli's equation). But is this really true? For instance, in Toricelli's result, the velocity(f) is different from the velocity(i), but the Pi and Pf values are the same. Thus the fluid has experienced a change in velocity, but there is no difference in pressure. Am I misunderstanding this concept? Thank you all so much in advance!

 

[Studiot]

Good morning, miaou5 and welcome to Physics Forums.

There is always a force associated with an acceleration

Force = mass x acceleration = rate of change of momentum (Newton 2)

This force can arise in many ways. In the case of fluid motion it arises from pressure difference or momentum transfer.

Don't forget that acceleration and momentum are a vector quantities so change of direction qualifies for the generation of force as well as change of magnitude.

Bernoulli's equation is a statement of energy conservation. In the absence of an external agent energy is constant. This is often measured as 'pressure head' (a measure of potential energy).

In this form B states that the sum of the pressure heads due to static potential energy, gravitational potential energy and kinetic energy are constant for a given parcel of fluid.
So if the fluid accelerates The kinetic head increases and one or both of the other two decrease.

I do not know what Pi and Pf are, you should always predefine your symbols before using them.