If the aim is to let a 700 kg pump flout on the surface of water, how many cylinders ( 50cm*90cm ) containing fresh water should we have ?
To determine the number of cylinders containing fresh water needed to let a 700 kg pump float on the surface of water, we can follow these steps:
Step 1: Calculate the volume of the pump.
To achieve buoyancy and make the pump float, the weight of the displaced water must be equal to or greater than the weight of the pump. We can calculate the volume of the pump using the formula:
Volume = Mass / Density
Assuming the density of water is 1000 kg/m^3, we have:
Volume = 700 kg / 1000 kg/m^3
Volume = 0.7 m^3
Step 2: Calculate the volume of one cylinder.
The volume of a cylinder can be calculated using the formula:
Volume = π * radius^2 * height
Given the dimensions of the cylinder, we have:
Radius = (50 cm / 2) = 0.25 m
Height = 0.9 m
Volume of one cylinder = π * (0.25^2) * 0.9
Volume of one cylinder ≈ 0.1768 m^3
Step 3: Calculate the number of cylinders.
To find the number of cylinders needed, we divide the volume of the pump by the volume of one cylinder:
Number of cylinders = Volume of pump / Volume of one cylinder
Number of cylinders = 0.7 m^3 / 0.1768 m^3
Number of cylinders ≈ 3.96
Since we cannot have a fraction of a cylinder, we need to round up to the nearest whole number. Therefore, you would need to have at least 4 cylinders containing fresh water to let a 700 kg pump float on the surface of the water.