Calculating Pressure in a Pipe with Different Diameters

[JBemp]

Dont know if this is the right forum but here goes



In a pipe with a diameter 0.15 there is a smaller area with the diameter 0.075

imagine a pipe with one part twice as small then after the smaller part its the larger size agian

point A 0.15 smaller part point B 0.075

The speed of the fluid at point A is 1m/s

the statik pressure in the pipe is 1 Bar at point A

waters density is 1000 kg/m^3

I know the dynamik pressure is 500Pa at point A

I need to find the statick pressure after point B



I used Bernoullis formula

i don't know were the sign for row is on my cpu so i will use @

@*C^2/2+@*g*h+P1=@*c^2/2+@*g*h+P2

I know i can cross out @*g*h



Anyways this is as far as i got could somone please check my work

P2=500+100000-(1000*(2^2/2)) unsure if it is 2^2/2

= 98500pa


Also sorry for the spelling am swedish :)

 

[jbsteele]

Yes, your calculation is correct. The equation you used is Bernoulli's equation, which states that the sum of the pressure, kinetic energy and potential energy of a fluid in any two points along a streamline is constant. You can rearrange the equation to solve for the pressure at point B: P2 = P1 + (ρ*V1^2/2) - (ρ*V2^2/2), where ρ is the density of the fluid, and V1 and V2 are the velocities at points A and B, respectively. In this case, P1 = 1 bar, V1 = 1 m/s, V2 = 0 (since the velocity is zero after the smaller part), and ρ = 1000 kg/m3. Substituting in these values gives P2 = 98500 Pa.

 

[nlightner]

First of all, it is important to note that the pressure in a pipe is not solely dependent on the diameter, but also on the flow rate and other factors such as the fluid's viscosity and the pipe's material and shape. Therefore, simply knowing the diameter of the pipe is not enough to accurately calculate the pressure.

That being said, let's assume that the flow rate and other factors remain constant. In that case, your calculation using Bernoulli's formula seems correct. However, it is important to note that the units must also be consistent. In your calculation, the units for velocity are in meters per second (m/s), while the units for density are in kilograms per cubic meter (kg/m^3). This inconsistency can affect the accuracy of your result.

Additionally, it is important to mention that the pressure at point B will not be exactly 98,500 Pa. The pressure will decrease gradually as the fluid moves from point A to point B due to friction and other factors. Therefore, the pressure at point B will be slightly lower than 98,500 Pa.

In conclusion, while your calculation using Bernoulli's formula is a good starting point, it is important to consider other factors and make sure that the units are consistent in order to get a more accurate result. It is also recommended to double check your work and possibly consult with a colleague or expert in the field to ensure the accuracy of your calculations.