# Bernoulli's equation basics

While deriving the Bernoulli's equation, we write the change gravitational potential energy as $$mg(h' - h)$$ , say where $$m$$ is the mass and $$h'$$ and $$h$$ are the two heights. Why we don't consider the centre of mass in this case? I mean why we don't have this term written as $$\frac{mg(h' - h)}{2}$$. I feel I am having some problem in understanding some concept.

• The center of mass of what? – PiKindOfGuy Feb 27 '19 at 12:09
• The change of height is from h to h', not h to the average height of h and h'. The difference of 13 and 17 (mean is 15) is 4, not 2. – helpme Feb 27 '19 at 12:15
• @helpme in what places do we use the centre of mass concept? I need some examples. – Akash Roy Feb 27 '19 at 12:21
• @AkashRoy: in what places do we use the centre of mass concept? The attractive force (gravity) between two uniform bodies, e.g. For Bernoulli, $\Delta h$ is the difference in height along a flowline. – Gert Feb 27 '19 at 14:26
• @Gert , I want to give you a situation . If we consider a U-shaped limb in which the left limb is filled with water upto a height say $h$ and the other has a height say $h1$. The limb has a valve in between to restrict any kind of flow of water. Say $h$>$h1$ . Then what should be the initial potential energy of the water in left limb? Considering $A$ as cross sectional area and the U-shaped limb is uniform. Assuming density is $d$. Say I will be opening the valve after sometime and the level equalises – Akash Roy Feb 27 '19 at 14:42