Calculus

posted by .

A cylindrical water tank has a radius of 2 feet and a height of 6.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft3.]

  • Calculus -

    Height of tank=
    H=6'
    Total volume of water
    V=πr²H
    Total mass
    m=ρV
    Average height raised
    h=H/2 (from centre of gravity to top)
    Total work done
    =mgh
    g=acceleration due to gravity
    =32.2 ft.s-2

    Note:
    If the water is supposed to load a truck below the tank, a pump is necessary to start filling the hose to the top and down, after that, water will flow up the tank, and down to the truck by gravity.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus (Definite Integrals - Work)

    Recall that work is defined to be force times distance, and that the weight (force) of a liquid is equal to its volume times its density. A fish tank has a rectangular base of width 2 feet and length 6 feet and sides of height 5 feet. …
  2. Calculus 2

    Calculus 2. Tom and Mike have a bet as to who will do the most work today. Mike has to compress a coil 200 feet. It takes Mike 250 lbs to compress the coil 10 feet. Tom needs to pump water through the top of a cylindrical tank sitting …
  3. Calculus 2

    Consider a trough with triangular ends where the tank is 10 feet long, top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3, and pump …
  4. Calculus

    A cylindrical water tank has radius r=1 meter and height 10 meters. Suppose the tank is lying on its side and is filled halfway with water. How much work does it take to pump all the water out the top of the tank?
  5. Calculus Applied Integrals

    A cylindrical tank of 22.1m high with radius 12.2m is filled to 10m high with water. How much work must be done to pump all the water out of the tank?
  6. Calculus

    Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small …
  7. CALCULUS

    Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small …
  8. Calculus

    A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?
  9. calculus

    A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?
  10. Calculus

    A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?

More Similar Questions