A 300L water tank is 2.8m above the ground and constantly refills itself to always have 300L present. A pipe with a diameter of 12.5mm runs from it to the shower. Due to gravity, work out how many litres per minute are produced?
To work out the number of liters per minute produced by the water tank, we need to consider the flow rate of the water through the pipe.
We can use Torricelli's law to calculate the flow rate, which states that the velocity of a fluid flowing out of a hole in a container is given by the equation v = √(2gh), where v is the velocity of the fluid, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the water column above the hole.
In this case, the height h is 2.8 meters, and we need to convert it to meters per second since we want our answer in liters per minute. So, we need to find the velocity of the water as it leaves the tank.
v = √(2gh)
v = √(2 * 9.8 * 2.8)
v ≈ √(54.64)
v ≈ 7.4 m/s
Now that we have the velocity of the water, we can calculate the flow rate. The flow rate (Q) is given by the formula Q = Av, where A is the cross-sectional area of the pipe and v is the velocity.
First, let's calculate the cross-sectional area of the pipe. Since the diameter is given, we can find the radius (r) by dividing the diameter by 2: r = 12.5 mm / 2 = 6.25 mm = 0.00625 m.
The cross-sectional area (A) of the pipe is then given by A = πr^2.
A = π * (0.00625)^2
A ≈ 0.000123 m^2
Finally, we can calculate the flow rate:
Q = Av
Q = 0.000123 * 7.4
Q ≈ 0.000909 m^3/s
Since the question asks for the flow rate in liters per minute, we need to convert m^3/s to L/min.
1 m^3/s = 1000 L/s
1 min = 60 s
Therefore, the flow rate is:
0.000909 m^3/s * 1000 L/s * 60 s/min ≈ 54.54 L/min
So, approximately 54.54 liters per minute are produced by the water tank.