Finding speed of water flowing in a pipe with changing diameter

1. Nov 21, 2012

aija

1. The problem statement, all variables and given/known data
Water flows in a pipe with speed 1.5 m/s at point 1.
The diameter of the pipe at point 1 is 4cm and the diameter at point 2 is 3cm.
density of water: 998.2071 kg/m^3
What's the speed of the water at point 2?

2. Relevant equations
I think you need to use this. I just have no idea how to find pressures p_1 and p_2 which seems to be needed to get the solution v2 out of this:
p_1+0.5ρ(v_1)^2 = p_2+0.5ρ(v_2)^2

3. The attempt at a solution
Trying to find the pressure difference p_2 - p_1
At this point I realize it's impossible because you need to use the equation above and it's also needed to solve v_2. No idea what else I could do.

2. Nov 21, 2012

Staff: Mentor

If you assume conservation of matter (water will not spontaneously appear or disappear in the pipe system) and unchanging density then what can you say about the volumetric rate of flow of water past any two given points? Can you calculate the rate of flow?

3. Nov 22, 2012

aija

Thank you I got it. So the volume flow rate vA is constant so
v_1*A_1=v_2*A_2
V_2=-(v_1*A_1)/A_2

Last edited: Nov 22, 2012
4. Nov 22, 2012

aija

Still getting a wrong answer. Is something wrong in my equation?

with values
A_1 = 3.5 cm
A_2 = 2.5 cm
v_1 = 2.0 m/s

i get 2.8 m/s and it's wrong.

the correct answer was 3.9 m/s. But why did I get a wrong answer?

Last edited: Nov 22, 2012
5. Nov 22, 2012

Staff: Mentor

Those look like different values from those in your original post. Are A_1 and A_2 supposed to be cross sectional areas or diameters? (The given units suggest diameters).

If they are diameters then they lead to a result of 3.92 m/s .

6. Nov 22, 2012

aija

Oh thanks. I accidentally used diameters as areas...