What is the fluid velocity in a restriction using Bernoulli's principle?

[fro]

Liquid flows through a 4cm diameter at 1m/s. There is 2cm diameter restriction i n the line. Find fluid velocity in restriction.

$$p_1+ \rho\cdot g \cdot y_1 + \frac{1}{2}\rho \cdot(v_1)^2 = p_2+ \rho \cdot g\cdot y_2 + \frac{1}{2}\cdot \rho\cdot(v_2)^2$$

I know I have to use Bernoulli's principle to solve this. I am confused as to if I use the diameter or radius in the problem for the height. Can I cancel out p1 and p2?

 

[radou]

Unless I'm missing something, you could solve this by simply stating A1v1 = A2v2, where A1 and A2 are the areas of the cross sections of the pipe.

 

[fro]

Unless I'm missing something, you could solve this by simply stating A1v1 = A2v2, where A1 and A2 are the areas of the cross sections of the pipe.

Thanks, I got it.

 

[fro]

Here is a slightly different one:
Water flows at 12m/s with pressure of 3X10^4 N/m^2. If the pipe widens to twice its original radius, what is the pressure in the wider section?

I am trying to plug everything to Bernoulli's principle. Problem is that both the pressure and radius is unknown. Any hints as to how I should start this problem? Thanks.

 

[radou]

Here is a slightly different one:
Water flows at 12m/s with pressure of 3X10^4 N/m^2. If the pipe widens to twice its original radius, what is the pressure in the wider section?

I am trying to plug everything to Bernoulli's principle. Problem is that both the pressure and radius is unknown. Any hints as to how I should start this problem? Thanks.

Again, use the equation (i.e. conservation of mass) you used to solve the first problem, and then you'll have everything you need to apply Bernoulli's equation and solve for the pressure in the wider section.