Two liquids are in a static equilibrium. Water pw= 998 kg/m^3 is in the right arm. Oil in the other. Given l=120mm and d=15mm, what is the density of the oil?
To find the density of the oil in this scenario, we can use the principle of static equilibrium for fluids. The principle states that the pressure at any given point in a fluid is equal to the pressure exerted by the column of fluid above it.
In this case, we have two liquids in a U-shaped tube: water in the right arm and oil in the left arm. The heights of the water and oil columns are not given, but since the system is in static equilibrium, we can assume that the pressures exerted by each liquid at the same level are equal.
Let's denote the density of the oil as po. The pressure exerted by the oil column is given by the formula P = po * g * h, where g is the acceleration due to gravity and h is the height of the oil column.
Similarly, the pressure exerted by the water column is given by P = pw * g * h, where pw is the density of water.
Since the pressures are equal, we can set up the following equation:
po * g * h = pw * g * h
The acceleration due to gravity (g) and the height (h) are common on both sides of the equation, so we can cancel them out:
po = pw
Substituting the given density of water (pw = 998 kg/m^3), we find:
po = 998 kg/m^3
Therefore, the density of the oil is also 998 kg/m^3.