Water flow speed through a pipe

[Capncanada]

Homework Statement

Water flows through a 1.3 cm diameter pipe into a 295 L bathtub, which it fills in 5 min.

What is the speed of the water in the pipe?

Homework Equations

V_in=v_L*t*A_L (Equation I got in my class lecture, I think its a variation of bernoulli's.)

The Attempt at a Solution

Solved for v_L in that equation, but that's not correct.

 

[SteamKing]

Did you check your units? You are given liters, cm, and minutes. What units are used for velocity?

 

[zgozvrm]

Clearly, the speed of the water in the pipe was
$$\frac{295\ \ell}{5\ min} = 59\ \ell/min$$

But, I'm guessing you're looking for linear speed, not volumetric speed? (something along the line of 5 cm/sec, for instance).

 

[RTW69]

Actually 59 l/min is the volumetric flow rate which will equal velocity * cross sectional area of pipe. To make the units turn out correctly you will need to convert liters to cubic meters

 

[asteriatic]

I would approach this problem by using the equation for volumetric flow rate: Q = A * v, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. We can rearrange this equation to solve for v: v = Q/A.

In this problem, we are given the diameter of the pipe (1.3 cm) and the time it takes to fill the bathtub (5 min), which gives us the flow rate (295 L/5 min = 59 L/min). We can convert the diameter to meters (0.013 m) and calculate the cross-sectional area of the pipe (A = π * r^2 = 3.14 * (0.013/2)^2 = 0.000132 m^2).

Plugging in these values into the equation v = Q/A, we get:

v = (59 L/min) / (0.000132 m^2) = 447,000 m/min

However, this is the velocity in meters per minute, and it may be more useful to convert it to a more common unit like meters per second. To do this, we can divide by 60 (to convert minutes to seconds) and by 1000 (to convert liters to cubic meters):

v = (447,000 m/min) / (60 min) / (1000 L/m^3) = 7.45 m/s

Therefore, the speed of the water in the pipe is 7.45 meters per second. It is important to note that this is an average speed, as the velocity of the water may change throughout the pipe due to factors such as friction and turbulence.