- #1
Logic hunter
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Consider a conventional U-tube with both the vertical tubes having the same uniform cross section area A and the horizontal tube of length L, connecting those tubes containing an ideal liquid. Now the free surfaces in both the vertical tubes will be at the same height and will have pressure equal to P0. Now if put a piston on anyone of the free surface and apply a force on it such that the pressure due to it on the surface of liquid just below it is F/A, then since at t=0 the liquid will still have 0 instaneous velocity so i can apply pascal's law according to which the pressure of each of the points will increase by F/A - P0 (P0 being the atompheric pressure.) So the pressure of the free surface in the other tube will also become F/A and on making FBD of any continuous liquid section the net force acting on it due to pressure will be same as the net force that was acting on it before the piston was used since pressure increased by same magnitude for all of the points i.e. net force would be zero so it will not have acceleration in any direction and won't start moving. So does this imply that pascals law would not hold true at this instant even if the liquid is at instantaneous rest. So what will happen? Also can i apply Bernoulli theorem once the liquid starts moving to analyse its properties ?