Question

A 15 cm centrifugal pump delivers 6 lps at a head of 26 m running at a speed of 1350 rpm. A similarly designed pump of 20 cm size runs at the same speed. What are the most likely nearest magnitudes of discharge and delivery head provided by the latter pump?
1. 11 lps and 46 m 
2. 14 lps and 52 m
3. 11 lps and 52 m
4. 14 lps and 46 m 

Answer 1

Correct Answer - Option 4 : 14 lps and 46 m 

Concept:

The above problem can be solved by using the following model laws for different type of pumps

1. \(\frac{{{\rm{DN}}}}{{\sqrt {\rm{H}} }} = {\rm{Constant}}\)

\(2.{\rm{\;}}\frac{{\rm{Q}}}{{{\rm{N}}{{\rm{D}}^3}}} = {\rm{Co}}nstant\)

Now, let suffix ‘1’ denotes for pump 1 and ‘2’ denotes for pump 2.

Calculation:

Given that, D₁ = 15 cm; H₁ = 26 m; Q₁ = 6 lps, N₁ = 1350 rpm and D₂ = 20 cm

\(\frac{{{{\rm{D}}_1}{{\rm{N}}_1}}}{{\sqrt {{{\rm{H}}_1}} }} = \frac{{{{\rm{D}}_2}{{\rm{N}}_2}}}{{\sqrt {{{\rm{H}}_2}} }}\)

\(\frac{{15 \times 1350}}{{\sqrt {26} }} = \frac{{20 \times 1350{\rm{\;}}}}{{\sqrt {{{\rm{H}}_2}} }}\)

⇒ H₂ = 46.22 m

\(\frac{{{{\rm{Q}}_1}}}{{{\rm{D}}_1^3{{\rm{N}}_1}}} = \frac{{{{\rm{Q}}_2}}}{{{\rm{D}}_2^3{{\rm{N}}_2}}}\)

\(\frac{6}{{15_{}^3 \times 1350}} = \frac{{{{\rm{Q}}_2}}}{{20_{}^3 \times 1350}}\)

⇒ Q₂ = 14.22 lps