It has been suggested that for liquids. It has been suggested that for a liquid distributor for is equal to K in which is constant and S is the surface tension and beta is the compressibility show that K is not a dimensional constant.
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Proved that K = M^−1L^4T^2 and K is not a dimensionless constant.
Explanation:
- Surface tension is force per unit length.
- Dimension of Force is M^1L^1 T^−2, divided by length we get the dimensional formula of surface tension is M^1 L^0 T^−2.
- Compressibility is the fractional change in volume per unit increase in pressure.
Dimension of compressibility is M^−1L^1T^2.
[S] = M^1L^0T^−2
[β] = M^−1L^1T^2
S3β4 = K[M^3L^0T^−6 M^−4L^4T^8] = K
K = M^−1L^4T^2
K is not a dimensionless constant.
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