Dimensional formula of surface tension, [S]=[M1L0T−2]
Dimensional formula of energy, [E]=[M1L2T−2]
Dimensional formula of velocity, [V]=[M0L1T−1]
By applying dimensional analysis,
S=EaVbTc
[M1L0T−2]=[M1L2T−2]a[M0L1T−1]b[T]c
[M1L0T−2]=MaL2a+bT−2a−b+c
On comparing,
a=1
2a+b=0⇒b=−2
−2a−b+c=−2⇒c=−2
∴S=E1V−2T−2