# 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.