Question

What is the maximum power available at the downstream end of a pipeline 3 km long, 20 cm in diameter, if water enters at the upstream end at a pressure of 720 m of water, with taking pipe friction coefficient as 0.03 and g as 10 m.s${}^2$?

• A. 370 mhp
• B. 340 mhp
• C. 375 mhp
• D. 325 mhp

Answer 1

The correct option is D 325 mhp

$h_f=\frac{H}{3}=\frac{720}{3}=240m$

$H_{exit}=\frac{2H}{3}=480m$

$h_f=\frac{8Q^2\times F\times L}{{\pi }^{2}g\times D^5}$

$240=\frac{8Q^2\times 0.12\times 3000}{{\pi }^{2}g\times {0.2}^5}$

$\Rightarrow Q=0.0508m^3/s$

$P_{exit}=\rho Qg{H}_{exit}$

$=\frac{1000\times 0.508\times 9.81\times 480}{735.5}$

= 325.31 mhp

Alternatively

In this problem, the value of friction factor is not defined properly. Friction coefficient is given as point 0.03 if we taken f = 0.33, where f is friction factor then,

$h_f=\frac{8Q^2\times f\times L}{{\pi }^{2}g{D}^5}$

$240=\frac{8Q^2\times 0.03\times 3000}{{\pi }^{2}g\times {0.2}^5}$

$\Rightarrow Q=0.102m^3/s$

$P_{exit}=\rho Qg{H}_{exit}$

$=\frac{1000\times 0.102\times 9.81\times 480}{735.5}$

= 653.02 mhp