pascal's law?

Question

to demostrate it, we have been shown a round bottomed flask with several holes(4) and vertical tubes coming out of them in which intial water seeks its level....then there is a piston on the cork,which when we press,jets of water come out from the nozzels of the tubes ...the jets of water reache the same height...

i wanted to know....it is written in the book that 'jets of water will reach the same height'....HOW?....the pressure applied by the piston here has travelled throughout....but the mass in the lowest column(highest column) is much more ...than the mass in the other columns....so as f=ma...force = mass*acc;

thus,....the acceleration in the lower one shud be least and the acc in the highest (lowest heighted column) shud be most coz of mass.....so how can they reach the same height in the same time?

plz explain

listen,...i am asking bout time...the TIME in which the jets of water will reach the height...the one with the more mass...has got to have it slower...isnt it?

OK...BUT I AM TALKING OF TIME???
WHAT BOUT THE RATE OF AQUIRING EQUILIBRIUM???

akshay, i COULDNT find an answer for my queries in ur questions....the questio u have asked on pascals is different from mine

Answer 1

F=ma ... true.

but the "m" that you need to consider and the "F" you need to consider have to be defined more precisely.

first of all, the pressure is defined as force per unit area, which means that the larger the area, more the force. in the case of a larger hole for example, the force is greater as a total.

however, you can think of it in another way as well. think of single molecules of water and the force each of them apply to its neighbor (which in turn jumps out of the hole) since the pressure you apply by the piston is constant, the force on all the molecules is the same at the same height.

This means that you have to take the mass of individual molecules and the force on each of those molecules in order to use F=ma correctly. (even if the motion is totally chaotic and require much more complicated calculations - especially after the water leaves the holes)

Since everything is the same for all the molecules, the time will be the same as well.

Answer 2

The pressure here is the force per unit area. So the total force on each different cross section will be the pressure , which is constant through out the entire liquid in the flask, times the cross sectional area. Hence the columns of water will reach the same height. More water more force same height.

Answer 3

catty i want to explain u but i could not understand the Question.

this is answer for what i understood becoz atmospheric pressure acts equally on water in tubes of what ever may be the size

Answer 4

catty ive already asked this question so if you want details check it out in my questions and yes you will also understand the time taken by the jets of water