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we know that by F=dP/dt=vdm/dt=pav^2

where p is density and P is momentum.considering the hole really small compared to the container.

however by Bernoullis equation Pressure(inside)= Presure(atm) + 1/2pv^2

i.e difference in pressure = pgh = 1/2pv^2

so force on container should be (difference in pressure)*(Area of cross section)= 1/2pv^2

these two do not match and every book suggests the first one.

Can someone help me(and tell me what is wrong with the second approach)

Thanks in advance

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  • $\begingroup$ Are you familiar with the macroscopic momentum balance equation? $\endgroup$
    – Chet Miller
    Commented Dec 6 at 12:10
  • $\begingroup$ we know that by F=dP/dt=vdm/dt=pav^2 Where has this equation come from? Is v constant? Does it not change from 0 to v? $\endgroup$
    – Farcher
    Commented Dec 6 at 16:21
  • $\begingroup$ @ChetMiller I dont think so. I am in high school $\endgroup$
    – Kshitij
    Commented Dec 7 at 12:26
  • $\begingroup$ When you wrote your first "we know" equation, where did it come from. $\endgroup$
    – Chet Miller
    Commented Dec 7 at 12:28
  • $\begingroup$ @ChetMiller I thought of it this way Fdt=dm(change in velocity) this would be due to elementary dm mass. $\endgroup$
    – Kshitij
    Commented Dec 7 at 14:28

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