If it takes 2.45 min to fill a 24.5 L bucket with water flowing from a garden hose of diameter 2.70 cm, determine the speed at which water is traveling through the hose.
What is volume/time*1/area?
change minutes to seconds
change Liters to cm^3 (ie, 24500cm^3) Your answer will be in cm/second
To determine the speed at which water is traveling through the hose, we can use the formula for the volume flow rate:
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.
First, let's calculate the cross-sectional area of the hose using its diameter:
A = π * (d/2)^2
Given that the diameter of the hose is 2.70 cm, we can calculate the area:
A = π * (2.70 cm/2)^2
Next, convert the area to square meters since the units of the flow rate will be in cubic meters per second:
A = π * (0.027 m/2)^2
Now, let's determine the volume flow rate by rearranging the formula:
Q = V / t
Where Q is the volume flow rate, V is the volume (24.5 L), and t is the time (2.45 min).
Convert the volume to cubic meters:
V = 24.5 L = 0.0245 m³
Convert the time to seconds:
t = 2.45 min = (2.45 * 60) s = 147 s
Now, substitute the values into the volume flow rate formula:
Q = (0.0245 m³) / (147 s)
Finally, plug in the value of the cross-sectional area to calculate the speed:
(0.0245 m³) / (147 s) = A * v
Solving for v:
v = Q / A
Substituting the values:
v = (0.0245 m³) / (147 s) / (π * (0.027 m/2)^2)
Calculating the value, the speed at which water is traveling through the hose is approximately equal to:
v ≈ 2.03 m/s