# What is the psi at the bottom of different tubes filled with water filled at the same height

if I have a 1 inch square tube with 144 feet of water I know I have about 63 pounds of water (63lbs ft**3) and 63 psi at the bottoms off the tube.

If I have a 1/4 inch sq tube filled with water at 144 feet. I know this is only 15.x lbs (i.e. 1/4 of above) of water total. If I measure this at the bottom across a 1 inch plate, I should only get 15 lbs of water. Yet I know from every other discussion that I will read 63 psi if I put a pressure meter on the bottom of that tube. Please provide the equation that clearly differentiates this logic. - Embarrassed Engineer.

• Force and pressure are different concepts. Apr 22, 2016 at 16:20

## 1 Answer

$Pressure = \dfrac{Force}{Area}$

Suppose your initial pressure is:

$P_1=\dfrac{F_1}{A_1}$

Now you make the cross sectional area of the tube have $\dfrac{1}{4}$ the initial area. And this makes the total volume, hence total mass and total force $\dfrac{1}{4}$ what it was. The two $\dfrac{1}{4}$'s cancel.

$P_2=\dfrac{(\dfrac{1}{4}F_1)}{(\dfrac{1}{4}A_1)} = P_1$

Force becomes a quarter what it was. But area also becomes a quarter what it was. So they cancel.