how much work does it take to pump water from a full upright tank circular cylindrical tank with radius 5m and a height of 10m to a level of 4m above the top of the tank
the work is what it takes to move the center of gravity of the water's weight the required height. The center of mass is h/2 meters below the top of the tank, so the distance to be moved is h/2 + 4 meters.
If d is the density of water, in kg/m^3, then mdg is the weight of the mass of water, and the work is
πr^2h * dg * (h/2 + 4)
To find out how much work it takes to pump the water, we can use the formula for work done against gravity:
Work = force × distance × height.
In this case, the force is the weight of the water, which can be calculated using the density of water and the volume of the cylinder. The distance is the height of the cylinder, and the height is the distance the water needs to be lifted.
Step 1: Calculate the volume of the cylinder
The volume of a circular cylinder is given by the formula V = π × r^2 × h, where r is the radius and h is the height.
V = π × 5^2 × 10
V = π × 25 × 10
V ≈ 785.4 m^3
Step 2: Calculate the weight of the water
The weight of water can be calculated using its density (ρ) and volume (V). The density of water is approximately 1000 kg/m^3.
Weight = density × volume
Weight = 1000 × 785.4
Weight ≈ 785,400 kg
Step 3: Calculate the work done
The work done against gravity is given by the formula Work = weight × distance × height.
Distance = height of the cylinder = 10 m
Work = 785,400 × 10 × 4
Work = 31,416,000 Joules
Therefore, it would take approximately 31,416,000 Joules of work to pump the water from the full upright tank with a height of 10m to a level of 4m above the top of the tank.
To calculate the work required to pump water from a tank to a higher level, we need to consider the change in potential energy of the water. The potential energy of an object is given by the formula: PE = m * g * h, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height difference.
In this case, the mass of the water can be determined using the formula for the volume of a cylinder: V = π * r^2 * h, where V is the volume, r is the radius, and h is the height.
So, the volume of the cylindrical tank is: V = π * (5^2) * 10 = 250π cubic meters.
To find the mass, we need to multiply the volume by the density of water, which is approximately 1000 kg/m^3. Therefore, the mass of the water is: m = 250π * 1000 kg.
The height difference is given as 4m, so h = 4m.
Lastly, the work required to pump the water to a higher level is the change in potential energy: Work = PE_final - PE_initial. In this case, the initial potential energy is zero, as the water is at the bottom of the tank.
So, the work required to pump the water is: Work = m * g * h = (250π * 1000) * 9.8 * 4 joules.
To calculate the final answer, you can use a calculator or computer software to evaluate the expression: (250π * 1000) * 9.8 * 4.
If I'm correct....
You would multiply pi times radius squared times height to get the volume of the cylinder tank.
3.14x25x14=____
3.14x25 is 78.5
And 78.5x14=______
Hope this helps