Two centrifugal pumps P and R are available for use in a pipe flow system and their head-discharge characteristics are as follows.

PUMP P PUMP R

Discharge (cumecs) Head (m) Discharge (cumecs) Head (m)

0 40 0 45

0.12 35 0.14 40

0.2 28 0.24 35

0.3 18 0.36 21

The following statements (S1, S2 and S3) pertain to the head and discharge values during actual operation. Neglect losses in the system.

Which of the following statements are correct?

S1: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 35 m.

S2: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 70 m.

S3: When the two pumps P and R are connected in series, the discharge is 0.3 cumec corresponding to a head of 46 m.

Question

Two centrifugal pumps P and R are available for use in a pipe flow system and their head-discharge characteristics are as follows.

The following statements (S1, S2 and S3) pertain to the head and discharge values during actual operation. Neglect losses in the system.

Which of the following statements are correct?

S1: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 35 m.

S2: When the two pumps P and R are connected in parallel, the discharge is 0.36 cumecs corresponding to a head of 70 m.

S3: When the two pumps P and R are connected in series, the discharge is 0.3 cumec corresponding to a head of 46 m.

rrbpapers · Accepted Answer

For pumps running in parallel (corresponding to a head of 35 m)

Q₁ = 0.12 m³/s, Q₂ =0.24 m³/s

Q_total = Q₁ + Q₂ = 0.36 m³/s

For pumps running is series (corresponding to a discharge of 0.3 m³/s)

H₁ = 18 m (given)

Applying linear interpolation between H value for Q = 0.24 m³/s and Q = 0.36 m³/s for pump 2.

H₂ = (35 + 21)/2 = 28 m

Total head, H_total = H₃ + H₂ = 46 m

S2 only