The pressure and flow rate characteristics of a fan operatin

The pressure and flow rate characteristics of a fan operating at 1800 hertz are given in the figure below. The curve is governed by the following relation: DP = 0.446332556 + 0.000377075887 middot V - 2.81006216 times 10^-7 middot V^2 + 5.41051541 times 10^-11 middot V^3 - 3.58974359 times 10^-15 middot V^4 Determine and plot the fan curve for rotational speeds of 900 and 2400 hertz. Determine and plot the power for the three speeds as a function of flow rate.

Solution

solution:

1)here for given fan characteristic equation relating head Hm and discharge V\' is given by

Hm1=.446+.0003*V\'-2.81*10^-7*V\'^-2+5.4105*10^-11*V\'^-3-3.5109*V\'^-4

2)where specific speed of fan is given by

Ns=N(V\')^.5/Hm^(3/4)

hence above is specific speed for this fan and it is same for all speed as it is geometric property .

for speed of N=1800 hz specific speed is

Ns=1800*(V\')^.5/Hm1^(3/4)

4)using same relation head for spped of N2=900 hz is

Hm2=(N/Ns)^(4/3)*V\'^(2/3)

putting value of Ns we get that

Hm2=.5^(4/3)Hm1=.3968*Hm1=.3968[.446+.0003*V\'-2.81*10^-7*V\'^-2+5.4105*10^-11*V\'^-3-3.5109*V\'^-4]

5)in same way head devloped for speed of N3=2400 Hz is

Hm3=(2400/1800)^(4/3)Hm1=1.4675Hm1=1.4675[.446+.0003*V\'-2.81*10^-7*V\'^-2+5.4105*10^-11*V\'^-3-3.5109*V\'^-4]

6)where power produced is given by

P1=density*g*V\'*Hm1

P1=density*g[.446V\'+.0003*V\'^2-2.81*10^-7*V\'^-1+5.4105*10^-11*V\'^-2-3.5109*V\'^-3]

7)here power related to P1 by

P2=P1(Hm2/Hm1)=.3968*P1=.3689[density*g[.446V\'+.0003*V\'^2-2.81*10^-7*V\'^-1+5.4105*10^-11*V\'^-2-3.5109*V\'^-3]]

P3=P1(Hm3/Hm1)=1.4675*P1=1.4675[density*g[.446V\'+.0003*V\'^2-2.81*10^-7*V\'^-1+5.4105*10^-11*V\'^-2-3.5109*V\'^-3]]

8)by using above formula we can easily get ploy for each case