Final answer:
To calculate the number of kilograms of water put on the fire in 30 minutes, you need to calculate the volume flow rate of the water through the underground pipe and convert it to liters per minute. Then, using the density of water, you can convert liters to kilograms to find the answer.
Step-by-step explanation:
To calculate the number of kilograms of water put on the fire in 30 minutes, we need to first calculate the volume of water that flows through the underground pipe in 30 minutes.
We can use the formula Q = Av, where Q is the volume flow rate, A is the cross-sectional area of the pipe, and v is the speed of the water.
Given that the diameter of the underground pipe is 100 cm and the speed of the water is 2.0 m/s, we can calculate the cross-sectional area using the formula A = πr^2, where r is the radius of the pipe.
The radius is half of the diameter, so the radius is 50 cm or 0.5 m.
Plugging in these values, we get A = π(0.5)^2 = 0.7854 m^2.
Now we can calculate the volume flow rate:
Q = Av
= 0.7854 m^2 × 2.0 m/s
= 1.5708 m^3/s
Since we want to calculate the volume of water flowing in 30 minutes, we need to convert the flow rate to liters per minute:
Q = 1.5708 m^3/s × 1000 L/1 m^3 × 60 s/1 min
= 94,248 L/min
To convert liters to kilograms, we need to know the density of water.
The density of water is approximately 1 kg/L. Therefore, the number of kilograms of water put on the fire in 30 minutes is:
94,248 L/min × 1 kg/L = 94,248 kg/min
Therefore, approximately 94,248 kilograms of water are put on the fire in 30 minutes.