Pressure vs Depth Incompressible fluids (liquids) When the pressure is much less than the bulk modulus of the fluid we treat the density as constant y1 independent of pressure incompressible fluid A For an incompressible fluid the density is the same everywhere mg F2 but the pressure is not Consider an imaginary fluid volume(a cube, face area A) The sum of all the forces on this volume must be zero as it is in equilibrium: F2-F1-mg=0 mg=Py、01A F=p2A →|p2=p1+pg(y2-y y,)Ag Physics 121: Lecture 20, Pg 5Physics 121: Lecture 20, Pg 5 When the pressure is much less than the bulk modulus of the fluid, we treat the density as constant independent of pressure: incompressible fluid For an incompressible fluid, the density is the same everywhere, but the pressure is NOT! Pressure vs. Depth Incompressible Fluids (liquids) Consider an imaginary fluid volume (a cube, face area A) The sum of all the forces on this volume must be ZERO as it is in equilibrium: F2 - F1 - mg = 0 y 1 y2 A p 1 p 2 F1 F 2 mg 0 p F2 − F1 = p2 A − p1 A mg = ( y2 − y1 )Ag p p g( y y ) 2 = 1 +  2 − 1