- - density of the liquid;
- - the height of liquid in the vessel;
- - paper, pen.
Derive the formula for the calculation of hydrostatic pressure.It is equal to the force acting perpendicular to the support area.In this case, the area of the support is the bottom of the vessel.The formula is written as follows: P = F / S.Since the liquid is at rest, the force acting on the bottom of the vessel, its weight is: F = W = mg, where m - mass of the liquid, g - free fall acceleration, which depends on the force of gravity.The coefficient g to planet Earth has designed and is 9.8 N / kg.If special accuracy in the calculation of pressure is not necessary, it is taken to be 10 N / kg.
Determine the mass of the liquid from the formula m = ρV
(where ρ - density of the liquid, V - the volume of liquid in the vessel).For rectangular container volume of fluid equal to its height multiplied by the area of the bottom, ie,V = Sh.If the vessel is cylindrical in shape, then instead of S is necessary to substitute the expression for finding the area of a circle: S = πr ^ 2, where π is equal to 3.14, and r - is the radius of the bottom of the vessel.
All formulas substitute in the basic formula P = F / S.The following expression: P = F / S = W / S = mg / S = ρVg / S = ρShg / S.The numerator and the denominator is the bottom area of the vessel S, so it can be cut.It turns out the formula P = ρgh.You can see that the hydrostatic pressure depends on the density of the liquid poured into the vessel and its height, but not on the bottom area of the vessel.This means that the bottom can be of any shape, not necessarily correct, but the vessel wall must be vertical.
Place a density value of the liquid and its height in the vessel in the derived formula P = ρgh and calculate the value of the hydrostatic pressure.To avoid confusion in the calculations, the unit of length (h) substitute in meters and weight of the fluid - in kilograms.If the condition of the problem you know, for example, the strength with which the fluid acts on the bottom of the vessel (by weight liquid), it is necessary to use the formula P = F / S = W / S.Under certain other data formula is derived similarly.
- pressure on the vessel wall formula