If you have a tank of water at sea level and the temperature of the water in the tank is 110 degrees F, what is the height of the water if the pressure at the bottom of the tank is 95 inches of mercury(absolute)
To determine the height of the water in the tank, we need to use the concept of hydrostatic pressure.
Hydrostatic pressure is the pressure exerted by a fluid due to the weight of the fluid column above it. This pressure increases with depth in a fluid and is given by the equation:
P = ρgh
Where:
P is the pressure
ρ (rho) is the density of the fluid
g is the acceleration due to gravity
h is the height of the fluid column
In this case, the pressure at the bottom of the tank is given as 95 inches of mercury (absolute), which means we need to determine the pressure in terms of inches of water column.
To convert pressure from inches of mercury to inches of water, we need to know the specific gravity of mercury and water. The specific gravity is the ratio of the density of a substance to the density of a reference substance. For mercury and water, the specific gravities are:
Specific Gravity of Mercury (Hg) = 13.6
Specific Gravity of Water = 1.0
Now, we can calculate the pressure in inches of water column:
Pressure (inches of water column) = Pressure (inches of mercury) x Specific Gravity of Water / Specific Gravity of Mercury
Substituting the given values:
Pressure (inches of water column) = 95 x 1.0 / 13.6
Once we have the pressure in inches of water column, we can use the hydrostatic pressure equation to solve for the height of the water column:
h = P / (ρg)
Since the density of water is approximately 62.4 lb/ft³, we can substitute the appropriate values:
h = Pressure (inches of water column) / (ρg)
h = (95 x 1.0 / 13.6) / (62.4 lb/ft³ x 32.2 ft/s²)
Simplifying the equation further, we find the height of the water column.