## Answers

Ans a) We know, System curve equation can be given as :

Hp = Z + H

where, Z = Static head = 20 m

H = head loss

=> Hp = 20 + H

At flow rate = 20 L/s or 0.02 /s.

Hp = 20 + 1() = 20 m

At flow rate = 40 L/s or 0.04 /s.

Hp = 20 + 4() = 20 m

Similarly we can calcultate head for all flow rates. Final results areshown in table below:

Q (Lit/s) | Hp (m) |

0 | 20 |

20 | 20 |

40 | 20 |

60 | 20.036 |

80 | 20.13 |

Plot the given system curve and performance curve as shown below :

**The point of intersection of performance curve and system curve is operating point or duty point.Hence,**

**Operating flow rate corresponding to duty point = 55 L/s or 0.055 s**

**Operating efficiency corresponding to opearting point () = 50%**

We know,

Power consumption (P) = g Q Hp /

where, Hp = Operating head corresponding to operating point = 20 m

Putting values,

=> P = 1000 x 9.81 x 0.055 x 20 / 0.50

**=> P = 21.58 kW**

**Ans b)** We know, when two similar pumps are conneted in series, the resulting performance head will be twice of head of individual pumps but flow rate remain same. Hence, performance curve for pumps in series is as follows :

Q (Lit/s) | Hp (m) |

0 | 50 + 50 = 100 |

20 | 45 + 45 = 90 |

40 | 33 + 33 = 66 |

50 | 25 + 25 = 50 |

60 | 14 + 14 = 28 |

Plot the given system curve and new performance curve as shown below

**The point of intersection of performance curve and system curve is operating point or duty point.Hence,**

**Operating flow rate corresponding to duty point = 63 L/s**

Hence, Maximum flow rate of proposed system is 63 L/s

**Ans c)** Now, for proposed system,

Q = 63 L/s or 0.063 /s

Hp = 20 m

Efficiency () corresponding to flow rate 63 L/s is approximate to 36%

Power consumption (P) = g Q Hp /

=> P = 1000 x 9.81 x 0.063 x 20 / 0.36

=> P = 34.34 kW

**Since, power consumption of system increases significantly (from 21.58 kW to 34.34 kW) but the increase in flow rate is small (from 55 L/s to 63 L/s), the proposed system is not suitable as the efficiency of system is very low.**

**please give upvote if you understood the answer**

**thank you**