# Relationship between turgor pressure and osmotic pressure?

I would like to know if there is a relationship between osmotic pressure (inside and outside of a cell) and turgor pressure. If so, is there a way to formalize it mathematically?

Eorn

Turgor Pressure(T.P) is defined as the amount of pressure inside a cell solely due to its water content, whereas Osmotic Pressure(Pi) is defined as the pressure required to stop osmotic flow between the cell and a pure solvent when the pressure exerted by water is zero.

Osmotic Pressure is often given as the negative of the Osmotic Potential(or Solute Potential) of the Cell.(Because more the solute, more pressure will be required to stop the osmosis, but against the gradient). (1)

Therefore, it can be easily seen that Osmotic Pressure is solely dependent on the solute concentration of the cell.

The Total Suction Pressure(S.P) of a Cell is the pressure required outside of a cell to stop the water flow in a pure solvent.

The T.P in such a situation would try to reduce the S.P (More the T.P, less would be the pressure on the outside). Whereas, the O.P in such a situation would try to increase the S.P (More the solute inside a cell, more would the water on the outside try to get on the inside)

Hence, Mathematically (considering no other pressures to be responsible for Total Suction Pressure)

S.P = Pi - T.P

This can Also be proved in the following way:

Water Potential(Psi W): Total Pressure inside a Cell.

Solute Potential/Osmotic Potential(Psi S): Reduction in Water Potential Magnitude due to addition of a Solute(solute reduces kinetic energy of water due to bonding)

Pressure Potential(Psi P): Hydrostatic Pressure, i.e, pressure exerted by the water present inside a cell if there were no solute particles.

By definition

Psi W = Psi S + Psi P

(We know, Psi S = -Pi) As written above in (1)

Psi W = -Pi + Psi P

(We know, Turgor Pressure is the same thing as Psi P)

Psi W = -Pi + T.P

Suction Pressure is the negative of Total Pressure inside a Cell

(S.P = -Psi W)

(Water flows from high water potential to low potential, but from low Suction Pressure to an area of High Suction Pressure)

Therefore

-S.P = -Pi + T.P

multiplying by -1

S.P = Pi - T.P