Calculate the pressure exerted halfway up a 30-ft tank. The liquid level in the tank is 22 ft. Specific gravity is 0.79. Vapor pressure at 100 degrees Fahrenheit equals 12.2 psi. The tank operates at 36 psi.
To calculate the pressure halfway up the tank, we need to consider the weight of the liquid in the tank and the vapor pressure.
Step 1: Calculate the pressure due to the weight of the liquid:
The pressure exerted by a liquid column is given by the equation:
Pressure = density x height x gravity
The density of the liquid can be calculated using the specific gravity (SG) and the density of water (ρw):
Density of liquid = SG x Density of water
The density of water is 62.4 lb/ft^3.
Density of liquid = 0.79 x 62.4 lb/ft^3
Next, we need to calculate the height of the liquid column halfway up the tank (22 ft / 2 = 11 ft).
Pressure due to the weight of the liquid = Density of liquid x Height x Gravity
Step 2: Consider the vapor pressure:
The vapor pressure is given as 12.2 psi.
Step 3: Calculate the total pressure:
The total pressure is the sum of the pressure due to the weight of the liquid and the vapor pressure.
Total Pressure = Pressure due to the weight of the liquid + Vapor pressure
Finally, compare the total pressure with the operating pressure of the tank (36 psi) to determine if it is within acceptable limits.
To calculate the pressure exerted halfway up the tank, we need to consider the hydrostatic pressure and the vapor pressure.
First, let's calculate the hydrostatic pressure. The hydrostatic pressure is caused by the weight of the liquid in the tank. The formula for hydrostatic pressure is:
P = ρ * g * h
where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column.
In this case, we are given the specific gravity, which is defined as the ratio of the density of the liquid to the density of water at a specified temperature. The density of water at 100 degrees Fahrenheit is approximately 62.4 lb/ft³. So, the density of the liquid (ρ) can be calculated as:
ρ = specific gravity * density of water
ρ = 0.79 * 62.4 lb/ft³
Next, we need to convert the height of the liquid column to the same unit as the density. Since the density is given in pounds per cubic foot (lb/ft³), we can express the height in feet.
Now, let's calculate the hydrostatic pressure:
P_hydrostatic = ρ * g * h
where ρ is the density of the liquid, g is the acceleration due to gravity (32.2 ft/s²), and h is the height (22 ft).
Next, let's calculate the vapor pressure. The vapor pressure is the pressure exerted by the vapor molecules above the liquid surface. In this case, the vapor pressure at 100 degrees Fahrenheit is given as 12.2 psi.
Finally, add the hydrostatic pressure and the vapor pressure to get the total pressure:
P_total = P_hydrostatic + vapor pressure
Now you can plug in the values and calculate the pressure exerted halfway up the tank.