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I am currently studying physiology, and in regards to the blood, we encounter many relations between volume, pressure, density etc, but of a liquid!!

I sometimes automatically go in my mind to the chemical equation of PV=nRT to apply it to the blood, but it was made about gases.

Would the same relations we see in gassesapply to blood? For example, higher pressure would mean lower volume? (Although it does not fit exactly to blood, cause increase in pressure of the blodstream in a given section of a vessel, could also increase that section's volume, [depending on the biological factors and type of vessel])

Basically I try to find logic and physical consistency when studying about hemodynamics etc.... but there are too many factors to consider that I can't formulate basic relations between volume, pressure, tension etc...

naturallyInconsistent
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user503965
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Short answer: no, ideal gas law doesn't apply to blood, and liquids, and not even to all gases in all conditions. Ideal gas law is a constitutive equation for rarefied gas.

To correctly represent the behavior of blood, you need its equations of state and constitutive equations, linking the thermodynamic variables of the system, and providing the expressions of transport coefficients as a function of them.

Basically I try to find logic and physical consistency when studying about hemodynamics etc.... but there are too many factors to consider that I can't formulate basic relations between volume, pressure, tension etc...

I suspect that you are not the first to study hemodynamics, so I'd suggest you to look for constitutive equation of blood, and tune the choice of the model on the level of accuracy you need.

basics
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