Why in free fall condition the length of water column in capillary tube is equal to length of tube?h=2Tcos theta /drg where h is rise in?
height ,T=SURFACE TENSION d=-DENSITY r=RADIUS OF TUBE AND g=ACCELERATION DUE TO GRAVITY explain from this formula how rise in height equal length of tube in FREE FALL CONDITION.THANKS
To understand why the length of the water column in a capillary tube is equal to the length of the tube in free fall conditions, we can start by examining the formula you provided:
h = 2Tcos(theta) / drg
In this formula:
- h represents the rise in height of the water column in the capillary tube.
- T is the surface tension of the liquid.
- theta represents the contact angle between the liquid and the wall of the tube.
- d is the density of the liquid.
- r is the radius of the tube.
- g is the acceleration due to gravity.
In free fall conditions, there is no gravitational force acting on the liquid column. So the term "drg" becomes zero.
When drg = 0, the formula simplifies to:
h = 2Tcos(theta) / 0
However, dividing by zero is undefined in mathematics. Therefore, we can consider that in free fall conditions, there is no rise in height of the water column.
Since there is no rise in height, the length of the water column in the capillary tube will be equal to the length of the tube itself. This is because the cohesive forces between the water molecules and the adhesive forces between the water and the walls of the tube are balanced, resulting in a stable, level column of water.
So, in summary, the length of the water column in the capillary tube is equal to the length of the tube in free fall conditions because there is no rise in height due to the absence of the gravitational force acting on the liquid column.