Question

3.5 capillary action figure 3.13 a liquid rises in a narrow tube because of capillary action, a result of surface tension and adhesive forces. figure 3.14 when cohesive forces between molecules of a liquid exceed adhesive forces, the level of the liquid in the capillary tube below the surface of the surrounding fluid. capillary action is the process of a liquid flowing in a narrow space without any external forces like gravity. in capillary tubes the diameter of the opening is very small, on the order of a hundredth of a centimeter. in fact, the word capillary means \hair - like.\ if such a tube is inserted into a fluid for which adhesive forces dominate over cohesive forces, the liquid rises into the tube, as shown in figure 3.13. the rising of the liquid in the tube can be explained in terms of the shape of the liquids surface and surface tension effects. the magnitude of this force is f = γl=γ(2πr) 3.14 the vertical component of this force due to surface tension is fv = γ(2πr)(cosϕ) 3.15 for the liquid in the capillary tube to be in equilibrium, this upward force must be equal to the weight of the cylinder of water of height h inside the capillary tube. the weight of this water is w = mg = ρvg = ρgπr²h 3.16 in equilibrium, fv = w (applying newtons second law for equilibrium), we have γ(2πr)(cosϕ)=ρgπr²h 3.17 solving for h gives the height to which water is drawn into the tube: h = 2γρgrcosϕ 3.18 grade. 12 physics if a capillary tube is inserted into a liquid in which cohesive forces dominate over adhesive forces, the level of the liquid in the capillary tube will be below the surface of the surrounding fluid, as shown in figure 3.14. an analysis similar to the above would show that the distance h to the depressed surface is derived. capillary tubes are often used to draw small samples of blood from a needle prick in the skin. capillary action must also be considered in the construction of concrete - block buildings because water seepage through capillary pores in the blocks or the mortar may cause damage to the inside of the building. to prevent such damage, the blocks are usually coated with a waterproofing agent either outside or inside the building. water seepage through a wall is an undesirable effect of capillary action, but there are many useful effects. plants depend on capillary action to transport water and nutrients, and sponges and paper towels use capillary action to absorb spilled fluids.

Explanation:

planation:

Step1: Identify given formula

We are given the formula for the height $h$ to which water is drawn into the tube: $h=\frac{2\gamma}{
ho gr\cos\phi}$, where $\gamma$ is the surface - tension coefficient, $
ho$ is the density of the liquid, $g$ is the acceleration due to gravity, $r$ is the radius of the capillary tube, and $\phi$ is the contact angle.

Step2: Analyze the problem context

Capillary action occurs when adhesive forces dominate over cohesive forces (liquid rises) or vice - versa (liquid depresses). The formula is derived from the equilibrium of the upward force due to surface tension and the weight of the liquid column in the capillary tube.

Answer:

The height $h$ to which water is drawn into the capillary tube is given by $h = \frac{2\gamma}{
ho gr\cos\phi}$ and is based on the balance of surface - tension force and the weight of the liquid column for equilibrium.