a 600 gallon tank is half-filled with water. a spigot is opened above the tank,
ID: 2831769 • Letter: A
Question
a 600 gallon tank is half-filled with water. a spigot is opened above the tank, and a salt solution containing 1.5 lb of salt per gallon of solution begins flowing into the tank at the rate of 3 gal/min. simutaneously, a drain is opened at the bottom of the tank allowing the solution to leave the tank at a rate of 1 gal/min. assume that the solution in the tank is perfectly mixed at all times.
a) what will be the salt content after t minutes?
b) how much salt will there be in the tank when the tank is full?
Explanation / Answer
Determine the water pressure at the bottom of a full, upright cylinder by dividing the volume by the product of pi (?) multiplied by radius squared (R^2): V = ?R^2. This gives the height. If the height is in feet, then multiply by 0.4333 to get pounds per square inch (PSI). If the height is in meters, multiply by 1.422 to get PSI. Pi, or ?, is the constant ratio of the circumference to the diameter in all circles. An approximation of pi is 3.14159.
Determine the water pressure at the bottom of a full cylinder on its side. When the radius is in feet, multiply the radius by 2 and then multiply the product by 0.4333 to get the water pressure in PSI. When the radius is in meters, multiply the radius by 2 and then multiply by 1.422 to get PSI.
Determine the water pressure at the bottom of a full spherical water tank by multiplying the volume (V) by 3, dividing it by the product of 4 and pi (?), taking the cube root of the result and doubling it: (3V/(4?))^(1/3). Then multiply by 0.4333 or 1.422 to get PSI, depending on whether the volume is in feet-cubed or meters-cubed. For example, a spherical tank of volume 113,100 cubic feet that's full of water has a water pressure at its bottom of (113,100 x 3/4?)^(1/3) x 2 x 0.4333 = 26.00 PSI.
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