# Physical meaning of same pressure on the same plan (hydrostatic paradox) with different weight above them [duplicate] In this picture the points on red have the same pressure because the weight of the fluid is the same above them. But according to pascal law the point on black must have the same pressure(both 3 points are on the same plan),but the weight of the fluid above the point on black isnt the same. So how do we explain this?

• The top of the horizontal tube exerts a force on the liquid in the region of the black point which stops the fluid flowing out. – Farcher Sep 17 '18 at 17:13
• So the pressure are equal on both points? That's right? – Maickel Tawdrous Sep 17 '18 at 17:17
• Yes because if the pressures at the same horizontal level were not the same the fluid would move. – Farcher Sep 17 '18 at 17:19
• But if we apply hydrostatic formula we willn't find the same pressure,because the height isnt the same on black point. Except we choose the surface in contact with air as (Z=0). – Maickel Tawdrous Sep 17 '18 at 19:46
• Possible duplicate of Pressure at base of 3 different dam designs – sammy gerbil Sep 19 '18 at 1:09

## 1 Answer

Part of the weight of each fluid is supported by the base of each of the two upper tanks. So, the only part of the weight that really matters is that situated directly above each of the lower tubes (as if they were each extended vertically upward). The weights of the fluid on the two sides within these more restricted regions would be the same. If you calculate the pressure at the red points, based on the amounts of overlying fluid, the pressures will be the same.

• If i undersant what you said, the pressure on the two red points are the same, but does the pressure in the black point is the same as in the red points? – Maickel Tawdrous Sep 17 '18 at 19:43
• Yes, the black point is in the same fluid and at the same depth as the two red points, so it is the same as at the red points. – Chet Miller Sep 17 '18 at 20:42
• I'm confused, does the pressure depend on the depth of a point or the height of the colum above it? – Maickel Tawdrous Sep 17 '18 at 21:40
• At hydrostatic equilibrium, the pressure varies with vertical position z according to the equation $dp/dz=-\rho g$, where $\rho$ is the density, and it is independent of horizontal position. – Chet Miller Sep 17 '18 at 23:13
• If dP=-(rho)*g*dZ but dZ depend on frame of reference, so pressure depend on frame of reference. But is more logicaly to remplace dZ by H which is the heigjt of the liquid above which apply pressure? – Maickel Tawdrous Sep 18 '18 at 16:30