A tank is filled with fresh water until there is a depth of 35 ft. Determine the pressure, psig,
at the bottom of the tank.
water weighs 62.43 lb/ft^3
psig = (35 ft) * (62.43 lb/ft^3) / (144 in^2/ft^2)
answer has two sig.fig.
To determine the pressure at the bottom of the tank, we can use the formula for pressure at a given depth in a liquid:
P = ρ * g * h,
where:
P is the pressure at the bottom of the tank,
ρ is the density of the liquid,
g is the acceleration due to gravity, and
h is the depth of the liquid.
In this case, since the tank is filled with fresh water, the density of water, ρ, is approximately 62.4 lb/ft³, and the acceleration due to gravity, g, is approximately 32.17 ft/s².
Plugging in the values, we have:
P = 62.4 lb/ft³ * 32.17 ft/s² * 35 ft.
Calculating this expression will give us the pressure at the bottom of the tank in pounds per square inch gauge (psig).
To determine the pressure at the bottom of the tank, we can use the concept of pressure due to the weight of a fluid. The pressure due to the weight of a fluid is given by the formula:
Pressure = density x gravitational acceleration x height
In this case, we need to know the density of water and the gravitational acceleration.
The density of water is approximately 62.4 lb/ft³, and the gravitational acceleration is approximately 32.2 ft/s².
Now, let's calculate the pressure at the bottom of the tank:
Pressure = 62.4 lb/ft³ x 32.2 ft/s² x 35 ft
Note that the units will cancel out, leaving us with psi (pound per square inch) as the unit for pressure.
The calculation will be as follows:
Pressure = (62.4 lb/ft³) x (32.2 ft/s²) x (35 ft)
Now, let's plug the values into a calculator to find the answer.
Pressure = 70,420.8 lb/ft²
To convert lb/ft² to psi, we need to divide the value by the conversion factor, which is 144.
Pressure = 70,420.8 lb/ft² / 144 = 488.06 psi
Therefore, the pressure at the bottom of the tank is approximately 488.06 pounds per square inch (psi).