Water flowing through a 1.9-cm-diameter pipe can fill a 500L bathtub in 5.1min. What is the speed of the water in the pipe?
area of pipe * speed of water = Q = flow volume/second
area = pi (.019)^2
volume = 0.5 m^3
time = 5.1*60 = 306
so
pi (.019)^2 V = .5 m^3/306 s
solve for V in m/s
I did:
Q=change in v/change in t
= (500L)/(5.1m)
= (500L)/ (306s)
= 1.6 L/s
convert > 1 L = 100 mL = 10^3 cm^3 = 10^-3 m^3... therefore I got 16 x 10^-4
v= Q/A = Q/(pi)(r^2)
v = 16x10^-4/(pi)(0.0955)^2
= 0.017
i am incorrect though
I get 1.45 m/s
Re-tried using your help...
(pi)(0.19^2)V= 0.5m^3/306s
(pi)(0.19^2)V= 0.016
V= 0.016/(pi)(0.19^2)
V= 8 x 10^-4
... i was incorrect
whoops I used diameter
use 4*1.45 = 5.8 m/s
.5/306 = .00163, not .0163
r = .019/2 = .0095
you have a decimal point off in the diameter too
Just follow my way using the diameter and multiply by 4 at the end. A = pi d^2/4
To find the speed of the water in the pipe, we can use the formula:
Speed = Volume / Time
First, let's convert the diameter of the pipe from centimeters to meters. Since 1 meter = 100 centimeters, the diameter of the pipe is 1.9 cm / 100 = 0.019 meters.
Next, we need to calculate the cross-sectional area of the pipe. The formula to find the area of a circle is:
Area = π * (radius)^2
The radius of the pipe is half of the diameter, which is 0.019 / 2 = 0.0095 meters.
So, the area of the pipe is:
Area = π * (0.0095)^2
Now we can calculate the volume of water that flows through the pipe. The volume of a cylinder (like the pipe) is given by the formula:
Volume = Area * Length
In this case, the length is not given, but it is not required to solve the problem. So, we can ignore it and focus on finding the speed of the water.
Now, let's substitute the values into the formula:
Volume = 500 L = 500 * 0.001 m^3 (since 1 L = 0.001 m^3)
Time = 5.1 min = 5.1 * 60 s (since 1 min = 60 s)
Now, let's calculate the speed:
Speed = Volume / Time
Speed = (500 * 0.001) m^3 / (5.1 * 60) s
By performing the calculations, we can find the speed of the water in the pipe.