Physics · Mechanical Properties Of Fluids · NEET
Pressure at a point depends only on the vertical depth of liquid above it: P = P0 + rho*g*h. Here h is the vertical height of liquid, not the amount of liquid. Two points at the same depth have the same column height above them, so the same pressure. This is why oddly shaped vessels (wide, narrow, slanted) connected at the bottom still show equal pressure at the same level. This is called the hydrostatic paradox.
More water means more weight, but that weight is spread over a larger base area. Pressure is force divided by area (P = F/A). The extra weight and the extra area increase together, so the pressure at the bottom stays the same. Only the vertical height h decides the pressure, not the total volume or weight of the liquid.
Yes. The rule 'same pressure' applies to points at the same horizontal level (same height) inside one connected body of the same liquid at rest. If two points are at different heights, the lower one has more pressure by rho*g*(height difference). Points not connected by the same fluid, or separated by a different liquid, may not follow this simply.
At the bottom where the tubes join, the fluid is one connected body, so the pressure there must be a single value. For the pressure at that junction to match from every side, each column must have the same vertical height of liquid above it. So the free surfaces settle at the same level. Builders use this idea with a transparent water pipe to mark equal heights on a wall.
For gases the same principle applies (pressure varies with height), but gas density is very small, so rho*g*h is tiny over normal heights. So in a small room the gas pressure looks almost equal at all heights. For liquids, rho is large, so the depth change matters a lot and you clearly see pressure grow with depth.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
In one connected fluid at rest, every point at the same depth (same horizontal level) has the same pressure, given by P = P0 + rho*g*h, where h is the vertical depth below the free surface.
No. Pressure at the bottom depends only on the vertical height of the liquid and its density, not on the shape, width, or total volume of the container.
It is the surprising fact that vessels of very different shapes and volumes, but the same liquid height, all have the same pressure at the bottom. It seems odd because they hold different amounts of water.
At the joined base, the fluid pressure must be one value. Equal pressure needs equal column height above, so the free surfaces of the same liquid rise to the same level in all connected arms.
Not directly. The simple equal-pressure rule needs the same continuous liquid. With two different liquids you must balance the pressures using each liquid's own density and height, as in a U-tube.
