Help with Bernoulli's equation for a central heating system

[ShaunG123]

Homework Statement

Scenario

You are required to show that the central heating system in a show house for a new estate has sufficient flow for upstairs and downstairs, to achieve the most effective heating possible.
The effective flow area in each radiator is 34 x 10-5 m2. The internal diameter of the pipes exiting the boiler is 25 mm and the internal diameter of all other piping is 15 mm.

The height from the boiler pump, situated in the garage beneath the first floor, to the downstairs radiators is 2.5 m (h2). The upstairs radiator is
2.75 m (h1) above the first floor radiators. The circulating fluid is a mixture of water and scale inhibitor, which has a relative density of 0.965.

If the average outlet pressure from the boiler is 1.7 bar gauge and the volume flow rate is 0.50 litres/second, calculate the pressure and velocity of the fluid in the system in the two different sized pipes and the radiators.

Relevant Equations

Bernoullis

so far I have found the velocity 1 and 2 by dividing the volume flow rate over the area which I got from pi x dia squared/4 my v1 = 1.01859m/s and v2= 2.82942m/s i have then figured out a pressure for the 15mm pipe which i got an answer of 2.71 bar however i am stuck on the rest of the question and how to find the radiators pressure and velocitie

 

[Andrew Mason]

Hi ShaunG. Welcome to PF!

If you can answer these questions, you should be able to figure out the pressure. What is the flow rate through the radiators? How is that related to area of the pipe (effective area is given) and velocity? How is pressure related to velocity?

AM

 

[BvU]

Hello Shaun, $\qquad$ $\qquad$!

v1 = 1.01859m/s and v2= 2.82942m/s

I assume v₁ is at the 15 mm pipe , v₂ is at the 25 mm, but what about the radiators ?
What is this 34 x 10^-5 m² anyway ?
And why not start writing down Bernoulli's equation using your variables ?

(I'll refrain from commenting on the 6 digits -- these are intermediate results.)

 

[ShaunG123]

Hi Andrew thanks for your reply all the information is in the above scenario I must calculate the velocities of each pipe which I have done and the pressure in the pipe and radiators. the velocities should be the same throughout the pipes I believe I am just unsure how to calculate the pressure and the velocity in the radiators. and do I actually need the radiator flow area (34x10-5) or is it just there to throw me

 

[Andrew Mason]

Hi Andrew thanks for your reply all the information is in the above scenario I must calculate the velocities of each pipe which I have done and the pressure in the pipe and radiators. the velocities should be the same throughout the pipes I believe I am just unsure how to calculate the pressure and the velocity in the radiators. and do I actually need the radiator flow area (34x10-5) or is it just there to throw me

Answer BvU's question about "what is this 34 x 10^-5"? If the flow rate through the radiators (volume/time) is x, how is x related to the effective cross-sectional pipe area (A) and velocity (v = ds/dt)? How is that related to pressure?

AM

 

[ShaunG123]

I believe you use that to find a velocity for the radiator using Q/FLOW AREA = VELOCITY therefore working pressure out with the remaining data

 

[Andrew Mason]

Correct

AM