Part (a): Discharge, Q = 12 L/s
Q=0.012 m3/s
Velocity heads
v22g=8Q2π2gD4
v122g=8(0.0122)π2(9.81)(0.154)=0.0235 m
v222g=8(0.0122)π2(9.81)(0.14)=0.119 m
Head lost
HLA−1=3×v122g=3(0.0235)=0.0705 m
HL2−B=20×v222g=20(0.119)=2.38 m
Energy equation between A and B
EA−HLA−1+HA−HL2−B=EB
(vA22g+pAγ+zA)−HLA−1+HA−HL2−B=(vB22g+pBγ+zB)
(0+0+0)−0.0705+HA−2.38=(0+0+72)
HA=74.4505 m
Output power of the pump
P=QγHA=0.012(9810)(74.4505)
P=8764.31Watts×(1hp/746Watts)
P=11.75 hp answer
Energy equation between A and 1
EA−HLA−1=E1
(vA22g+pAγ+zA)−HLA−1=(v122g+p1γ+z1)
(0+0+0)−0.0705=(0.0235+p1γ−6)
p1γ=5.906 m answer
Energy equation between 2 and B
E2−HL2−B=EB
(v222g+p2γ+z2)−HL2−B=(vB22g+pBγ+zB)
(0.119+p2γ−6)−2.38=(0+0+72)
p2γ=80.261 m answer
Checking
Energy equation between 1 and 2
E1+HA=E2
(v122g+p1γ+z1)+HA=(v222g+p2γ+z2)
(0.0235+5.906−6)+74.4505=(0.119+80.261−6)
74.38=74.38 (Check!)
Part (b): Discharge, Q = 36 L/s
Q=0.036 m3/s
Velocity heads
v22g=8Q2π2gD4
v122g=8(0.0362)π2(9.81)(0.154)=0.2115 m
v222g=8(0.0362)π2(9.81)(0.14)=1.0708 m
Head lost
HLA−1=3×v122g=3(0.2115)=0.6345 m
HL2−B=20×v222g=20(1.0708)=21.416 m
Energy equation between A and B
EA−HLA−1+HA−HL2−B=EB
(vA22g+pAγ+zA)−HLA−1+HA−HL2−B=(vB22g+pBγ+zB)
(0+0+0)−0.6345+HA−21.416=(0+0+72)
HA=94.0505 m
Output power of the pump
P=QγHA=0.036(9810)(94.0505)
P=33 214.87Watts×(1hp/746Watts)
P=44.52 hp answer
Energy equation between A and 1
EA−HLA−1=E1
(vA22g+pAγ+zA)−HLA−1=(v122g+p1γ+z1)
(0+0+0)−0.6345=(0.2115+p1γ−6)
p1γ=5.154 m answer
Energy equation between 2 and B
E2−HL2−B=EB
(v222g+p2γ+z2)−HL2−B=(vB22g+pBγ+zB)
(1.0708+p2γ−6)−21.416=(0+0+72)
p2γ=98.3452 m answer
Checking
Energy equation between 1 and 2
E1+HA=E2
(v122g+p1γ+z1)+HA=(v222g+p2γ+z2)
(0.2115+5.154−6)+94.0505=(1.0708+98.3452−6)
93.416=93.416 (Check!)