For the figure below calculate the pressures p1p4 knowing th

For the figure below calculate the pressures p1-p4 knowing that: Pa = 300 KPa Pb = 100 KPa The pressure drop between any two nodes ij is given by P_i - P_j = alpha_ijtimesq_ij alpha=128muL_if/d_if^2 mu = 0.1Pa.s Where Lij is the length of the pipe betw een nodes i and j and d is the diameter of the pipe between and j

Solution

2=128*0.1*200/(0.1*0.1) =256000 Pa.s/m

3=128*0.1*200/(0.1*0.1) =256000 Pa.s/m

5=128*0.1*150/(0.08*0.08) =300000 Pa.s/m

6=128*0.1*150/(0.08*0.08) =300000 Pa.s/m

Here 2/5 =3/6

=> balanced bridge=> no flow through 23 or q4=0;

hence

p1-p4=(200 kpa/(1+7+0.5*2+0.5*3))*(0.5*(2+3)) kpa

=(200/(177777.778+355555.556+278000))*278000 =68.529 kpa