Please answer fully and correctly and I will award points Problem 2 Consider a c
ID: 2997522 • Letter: P
Question
Please answer fully and correctly and I will award points
Problem 2 Consider a capillary glass tube tilted in water at angle Beta. The tube is open to air. The contact angle between water and glass is close to zero, so that sigma acting on the interfacial perimeter is along the tube. 1. Consider the concave-up interface between water and air as the free body diagram. The forces acting on the interface are: the interfacial force on the perimeter via surface tension, sigma, pressure force at point 1, just above the interface on the air side, pressure force at point 2, just below the interface on the water side. Express the foregoing statement using sum of forces equal to zero along the z-direction (tube centerline). 2. Write two hydrostatic relationships between P1 and Patm , and P2 and Patm . 3. Substitute P1, and P2 to derive an expression for the surface tension,Sigma.Explanation / Answer
Solution:
Capillary action is the result of cohesion between the water molecules, higher is the cohesion larger will be the surface tension and this parameter intern affects the capillary height in the tube.
The rise in the liquid height in the tube stops when there is a balance between the external pressure and the internal pressure.
Height in the capillary = 4(S) cos (t) / (row)gd
S = surface tension; t =contact angle and (row)=density of the liquid and d = diameter of the capillary tube
from the above problem:
contact angle = 0 (given) and from this information S = h(row)gd / 4
and increase in the 'd', shows more surface tension in the liquid also decrease in the height, because the drag of the water molecule along the tube inner surface decreases, this reflects as the decrease in the height.