Question 1: The surface tension of a liquid may be measured using the Pendant Drop Experiment....

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Question 1: The surface tension of a liquid may be measured using the Pendant Drop Experiment. In this experiment a drop of surface tension, a, and density, p is dangling statically from a fine capillary (small diameter) tube of radius R. The "light-bulb" shape of the droplet is due to competing gravitational and h(:) curvature forces. We study the water-air surface tension in STP conditions, as the fluid is injected precisely through an orifice of R, = 1mm. Ra a) Find the liquid pressure at the drop apex (z = 0). For this purpose, you may assume the droplet is spherical close to the apex (i.e., neglect the meniscus influence and use Ra). b) Write the stress balance at the interface for the problem and derive the differential equation and boundary conditions for the shape of the drop. Write every assumption you are taking. c) Assuming Ra/R, = 2, plot the shape of the pendant drop. Instructions: 1. Find the air and water properties at STP conditions 2. Solve the ODE found in (b) numerically. Please attach your code to your submission! 3. Write every assumption you are taking. d) We seek to investigate the influence of the surface tension on the drop shape. For that aim, artificially increase the standard surface tension by 5%, 10%, 25%, and 50%, and correspondingly plot the new shapes. e) A pendent drop occasionally breaks loose. This occurs when its weight exceeds the capillary force that holds it in place. Estimate the Ra/R, ratio for which the drop will break loose. (Hint: estimate the force balance on the drop, between its apex and neck.) Question 1: The surface tension of a liquid may be measured using the Pendant Drop Experiment. In this experiment a drop of surface tension, a, and density, p is dangling statically from a fine capillary (small diameter) tube of radius R. The "light-bulb" shape of the droplet is due to competing gravitational and h(:) curvature forces. We study the water-air surface tension in STP conditions, as the fluid is injected precisely through an orifice of R, = 1mm. Ra a) Find the liquid pressure at the drop apex (z = 0). For this purpose, you may assume the droplet is spherical close to the apex (i.e., neglect the meniscus influence and use Ra). b) Write the stress balance at the interface for the problem and derive the differential equation and boundary conditions for the shape of the drop. Write every assumption you are taking. c) Assuming Ra/R, = 2, plot the shape of the pendant drop. Instructions: 1. Find the air and water properties at STP conditions 2. Solve the ODE found in (b) numerically. Please attach your code to your submission! 3. Write every assumption you are taking. d) We seek to investigate the influence of the surface tension on the drop shape. For that aim, artificially increase the standard surface tension by 5%, 10%, 25%, and 50%, and correspondingly plot the new shapes. e) A pendent drop occasionally breaks loose. This occurs when its weight exceeds the capillary force that holds it in place. Estimate the Ra/R, ratio for which the drop will break loose. (Hint: estimate the force balance on the drop, between its apex and neck.)

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