dimensional formulae for surface tension S
Given S=<pgrh/2
Answers
Answer:
Surface tension is force per unit length.
Force = Mass × acceleration
Dimensions of force = M L T^-2
Therefore, the dimensions of Surface tensions = (MLT^-2)/L = M L⁰ T^-2
Let us use symbol T for surface tension.
The formula cited comes from determination of surface tension of a liquid, say water, from its rise in a capillary tube above the level of the liquid in a trough containing the liquid. Let the water rise in the capillary tube to a height h (in cm). The weight of column of water contained in the capillary tube of radius r = (volume of water) × (density of water) × (acceleration due to gravity) = (π r² h) × ( d ) × (g) = π r² h d g
This weight of water column is supported by the total vertical component of the force of surface tension acting all along the circumference of the water surface at height h = ( circumference of water surface in the capillary tube) × (vertical component of surface tence) = (2 π r ) × T Cos ß = 2 π r T Cos ß, where ß is the angle of contact. In liquids which wet the glass the angle of contact is small and Cos ß ~ 1. So total vertical upward force supporting the liquid column = 2 π r T
Equating the two forces we get
π r² h d g = 2 π r T
T = ½ r h d g
Dimensions of Surface Tension = Dimensions of radius of capillary tube r × dimensions of rise of water column h × dimensions of density × dimensions of acceleration due to gravity = (M⁰ L T⁰) × (M⁰ L T⁰) × ( M L^-³ T⁰) × ( M⁰ L T^-²) = M L⁰ T^-²
Dimensions of Surface tensions = M L⁰ T^-²
Surface tension is a force per unit length. Its units in cgs system are Dyne per centimetre and in MKS system are Newton per meter
Explanation:
S=pgrh/2
where:-
S=surface tension
g=acceleration due to gravity
r=radius
h=height
S=[M/L^3] [L1/T2] [L] [L]
S=MT^-2