30 Apr '14 00:55

I have to design a Duct system at work, The duct work basically looks like a 2 pronged fork. Something like this below ( please bare with me on this representation).

......| <--Inlet

....____ <-- Plenum

../........\

..|........|<--Duct outlets

On the left fork of the duct there will be 1 outlet, on the right fork there will be 2 outlets ( one on each side of the duct). All outlets will be slots along the length of of the section shown as "Duct outlets" above, and will all have the same cross-sectional area.

I am attempting to design the system such that the flows from each outlet are essentially equal. ( ie. 1/3 of the total system flow ).

I am attempting to generate a system curve from this configuration, by plotting the head loss, as a function of the volumetric flowrates Q_i, for each leg of the duct.

From continuity I know that in my left most duct (1) that

Q1 = 1/3*Qtot eq(1)

and, so the right most duct (2) must be

Q2 = 2/3*Qtot eq(2)

Using the Darcy-Weisbach equation ( temporarily ignoring component losses, for simplicity in getting my point across )

Head Loss (Q) = f1*1/(2g)*L1/D1*Q1^2/A1^2 + f1*1/(2g)*L1/D1*Q2^2/A2^2 eq(3)

Sub eq(1) & eq(2) ---> eq(3)

Assume round duct of Diameters D1 and D2 respectively

After simplification

H = ( f1*32/(9*pi^2)*1/g*L/D1^5 + f2*8/(9*pi^2)*1/g*L/D2^5)*Q^2 eq(4)

Fixing D1 in the above equation, I will Plot H(Q) for several specified D2, thus giving me a series of system curves based on a specific D2, over the entire domain of Q.

These can then be intersected with a specific fan curve ( giving a series operation points), and a duct size "D2" can then be selected from the the point of operation which corresponds to the desired system output.

My question to you: Is this a valid approach?

......| <--Inlet

....____ <-- Plenum

../........\

..|........|<--Duct outlets

On the left fork of the duct there will be 1 outlet, on the right fork there will be 2 outlets ( one on each side of the duct). All outlets will be slots along the length of of the section shown as "Duct outlets" above, and will all have the same cross-sectional area.

I am attempting to design the system such that the flows from each outlet are essentially equal. ( ie. 1/3 of the total system flow ).

I am attempting to generate a system curve from this configuration, by plotting the head loss, as a function of the volumetric flowrates Q_i, for each leg of the duct.

From continuity I know that in my left most duct (1) that

Q1 = 1/3*Qtot eq(1)

and, so the right most duct (2) must be

Q2 = 2/3*Qtot eq(2)

Using the Darcy-Weisbach equation ( temporarily ignoring component losses, for simplicity in getting my point across )

Head Loss (Q) = f1*1/(2g)*L1/D1*Q1^2/A1^2 + f1*1/(2g)*L1/D1*Q2^2/A2^2 eq(3)

Sub eq(1) & eq(2) ---> eq(3)

Assume round duct of Diameters D1 and D2 respectively

After simplification

H = ( f1*32/(9*pi^2)*1/g*L/D1^5 + f2*8/(9*pi^2)*1/g*L/D2^5)*Q^2 eq(4)

Fixing D1 in the above equation, I will Plot H(Q) for several specified D2, thus giving me a series of system curves based on a specific D2, over the entire domain of Q.

These can then be intersected with a specific fan curve ( giving a series operation points), and a duct size "D2" can then be selected from the the point of operation which corresponds to the desired system output.

My question to you: Is this a valid approach?