suppose you have a garden hose of diameter 2 cm and you use it to fill a 25 litre bucket with water. suppose it takes 1 minute to do that. what mass of the water will flow out of the hose into the bucket in that 1 minute? ?
Trick question, irritating
If you filled the bucket it is 25 liters. The density of water is about 1 kg/liter so about 1 kg.
I mean 25 kg of course.
To find the mass of the water flowing out of the hose into the bucket in 1 minute, we need to calculate the volume of water flowing through the hose and then convert it into mass.
First, let's calculate the volume of water flowing through the hose in 1 minute:
1. Calculate the cross-sectional area of the hose:
The diameter of the hose is given as 2 cm, so the radius (r) of the hose is half of that, which is 1 cm or 0.01 m.
The cross-sectional area (A) of the hose is given by the formula: A = π * r^2 = 3.14 * (0.01)^2 = 0.000314 m^2.
2. Calculate the volume of water flowing through the hose in 1 minute:
The rate at which water flows through the hose is usually given in terms of the volume flow rate (Q).
To calculate Q, we need to know the speed of the water flowing through the hose.
Since the speed is not given, let's assume a typical value of 1 meter per second (m/s).
Q = A * v,
where Q is the volume flow rate, A is the cross-sectional area of the hose, and v is the speed of the water.
Q = 0.000314 m^2 * 1 m/s = 0.000314 m^3/s.
3. Convert the volume flow rate to liters per minute:
1 m^3 is equal to 1000 liters.
So, 0.000314 m^3 is equal to 0.314 liters.
0.314 liters/s * 60 s/min = 18.84 liters/min.
Therefore, the volume of water flowing out of the hose into the bucket in 1 minute is approximately 18.84 liters.
Next, we need to convert the volume of water into mass:
1 liter of water has a mass of approximately 1 kilogram.
So, the mass of water flowing out of the hose into the bucket in 1 minute is approximately 18.84 kilograms.
To find the mass of water that will flow out of the hose into the bucket in one minute, we need to use the formula:
Mass = Volume x Density
First, let's calculate the volume of water that flows out of the hose in one minute. We know that the bucket has a volume of 25 liters, which is the same as 25,000 cubic centimeters (since 1 liter equals 1000 cubic centimeters).
The volume of water flowing out of the hose will depend on its diameter and the time it takes to fill the bucket. However, the diameter alone is not enough information to determine the flow rate. We also need to know the water pressure, length of the hose, and any restrictions or attachments on the hose, such as nozzles or sprinklers.
Once we have the flow rate (volume per unit time), we can multiply it by the time (1 minute) to get the total volume of water.
Assuming we have the flow rate, let's move on to calculating the mass.
The second factor we need is the density of water. The density of water can vary slightly with temperature, but for most practical purposes, we can assume it is approximately 1 gram per cubic centimeter (g/cm³).
Using the formula Mass = Volume x Density, we have:
Mass = 25,000 cm³ x 1 g/cm³
Mass = 25,000 grams
So, the mass of the water that will flow out of the hose into the bucket in one minute is 25,000 grams, which is equivalent to 25 kilograms.