If a 2-inch pipe will fill a tank in 6 hours, how long will it require for a 3-inch pipe to fill it?
"2-inch" and "3-inch" presumably refer to the diameter of the pipe, so the 3-inch pipe has (3/2)^2 or 2.25 times the cross-sectional area. Which means it can deliver fluid at 2.25 times the rate.
6 hours / 2.25 = 2 2/3 hours (2 hours and 40 minutes)
To find out how long it will take for a 3-inch pipe to fill the tank, we can use the concept of flow rate. The flow rate of a pipe is the amount of water that passes through the pipe per unit of time.
Let's assume that the flow rate of the 2-inch pipe is r, which means it can fill the tank in 6 hours. Therefore, in 1 hour, the flow rate of the 2-inch pipe would be 1/6 of the tank.
To determine the flow rate of the 3-inch pipe, we can use the concept of cross-sectional area. The flow rate of a pipe is directly proportional to its cross-sectional area.
The formula to calculate the cross-sectional area of a pipe is:
Area = π * (radius)^2
Since the diameter of the 3-inch pipe is larger than the diameter of the 2-inch pipe, the radius of the 3-inch pipe will be larger as well.
Let's denote the radius of the 2-inch pipe as r1, and the radius of the 3-inch pipe as r2. As the radius of the pipe increases, the flow rate also increases. So we can set up a proportion to determine the relationship between the flow rates of the 2-inch and 3-inch pipes:
Flow rate of 2-inch pipe / Flow rate of 3-inch pipe = (r1)^2 / (r2)^2
Since the flow rate of the 2-inch pipe is 1/6 of the tank per hour, and we want to find the time it takes for the 3-inch pipe, we'll let t represent that time.
Flow rate of 2-inch pipe = 1/6 tank / hour
Flow rate of 3-inch pipe = 1/6 tank / t
Setting up the proportion:
1/6 tanks / hour / (1/6 tanks / t) = (r1)^2 / (r2)^2
Simplifying:
t = (r2)^2 / (r1)^2
Since the diameter of a pipe is twice its radius, the radius of a 2-inch pipe is 1 inch, and the radius of a 3-inch pipe is 1.5 inches.
Plugging in the values:
t = (1.5^2) / (1^2)
t = 2.25
So, it will take approximately 2.25 hours for a 3-inch pipe to fill the tank.