How Do You Calculate the Height of Oil in a U-Tube?

[superjen]

A U-tube of circular diameter 5.60 mm initally contain just water. If 4.00 milliliters(cm^3) of oil is added to the left hand side of the tube the level of the oil is 6.8 mm higher than the level of the water in the right hand side of the tube. Determine the height of the oil.

i'd give some help, but I'm actually clueless on how to start this.

 

[LowlyPion]

A U-tube of circular diameter 5.60 mm initally contain just water. If 4.00 milliliters(cm^3) of oil is added to the left hand side of the tube the level of the oil is 6.8 mm higher than the level of the water in the right hand side of the tube. Determine the height of the oil.

i'd give some help, but I'm actually clueless on how to start this.

First start by converting the diameter of the inner tubing (which they give) to milli-liters of volume which is how much oil they add. i.e how many mm of height is 1 milliliter of volume.

Then draw a picture showing the oil standing higher (and how much below that the oil/water interface is).

 

[nlightner]

I would approach this problem by first identifying the known variables and their units. The diameter of the U-tube is given as 5.60 mm and the volume of oil added is 4.00 mL (or cm^3). The difference in height between the oil and water is also given as 6.8 mm.

Next, I would use the physical properties of the U-tube to determine the height of the oil. Since the tube is circular, we can use the formula for the volume of a cylinder (V=πr^2h) to relate the volume of the oil to its height. By rearranging the formula, we can solve for the height of the oil:

h = V/(πr^2)

Substituting the known values, we get:

h = 4.00 cm^3 / (π x (2.80 mm)^2) = 0.159 cm = 1.59 mm

Therefore, the height of the oil is 1.59 mm.

It is important to note that this calculation assumes that the diameter of the U-tube is constant along its entire length and that there is no air trapped in the tube. If these assumptions are not true, the calculated height may be slightly different from the actual height of the oil.