Solved Examples based on kaplan turbine

SOLVED EXAMPLES BASED ON KAPLAN TURBINE

Example - 41

A kaplan turbine working under a head of 30m developed 12000 kw shaft power. The outer diameter of the runner is 3.8 m and inlet diameter 1.8 m. The guide blade angle at the extreme edge of the runner is 35°. The hydraulic and overall efficiency of the turbine are 90% and 85% respectively. If the velocity of whirl is zero at outlet determine

(1) Runnet vane angle at inlet and outlet at the extreme edge of the runner. 

(2) Speed of the turbine

Given data:

To find:

1. Runner vane angle at inlet and outlet (θ & ϕ))

2. Speed of the turbine (N)

Solution:

5. From inlet velocity triangles

Result:

1. Runner vane angle at inlet θ =168.26° 

2. Runner vane angle at outlet ϕ = 9.10° 

3. Speed of the turbine (N) = 170.93 rpm

Example - 42

A kaplan turbine develops 24647.6kw power at an average head of 39m • speed ratio 2.0 and flow ratio of 0.61 diameter of the boss equal to 0.35 times the diameter of the runner and an overall efficiency of 90%. Calculate the diameter and speed of the turbine.

Given data:

Shaft power (S.P) = 24647.6 kw = 24647.6 × 103 w 

Head (H) = 39m

Diameter of the boss (Db) = 0.35 × Diameter of runner (D0)

Overall efficiency η0 = 90% = 0.9

To find:

1. Diameter of the runner D0, Db 

2. Speed of the turbine (N)

Solution:

Result:

1. Diameter of the runner D0 = 2.5m

2. Diameter of the boss (Db) = 0.875m

3. Speed of the turbine (N) = 422.61 rpm

Example - 43

The hub diameter of the kaplan turbine working under a head of 12m 0.35 times the diamger of the runner. The turbine is running at 100 rpm. If the vane angle of the extreme edge of the runner at outlet is 15o and flow ratio 0.6 find 

(1) Diameter of the tunner 

(2) Diameter of the boss

(3) Discharge through the runner and Vw2 = 0

Given data:

Head (H) = 12m

Speed (N) = 100 rpm

Hub diameter Db = 0.35 × D0

Vane angle of outlet ϕ = 15°

To find:

1. Diameter of the runner (D0)

2. Diameter of the hub (or) boss (Db)

3. Discharge through the runner (Q) 

Solution:

Result:

1. Diameter of runner (D0) = 6.55m 

2. Diameter of bass (Db) = 2.3m

3. Discharge (Q) = 272.04 m3/s

Example - 44

A kaplan turbine developed 14000 kw Power at 200 rpm the hub diameter is 1/3rd of runner diameter flow ratio 0.7 the hydraulic efficiency is 92% and overall efficiency is 84% designing for a specific speed of 300, determines.

(i) Net head available

(ii) Discharge rate 

(iii) Runner diameter

(iv) Guide vane angle

(v) inlet vane angle.

Given data:

Power (P) = 14000 kw = 14000 × 103 w

Speed (N) = 200 rpm

Hub diameter Db =1/3 D0

Hydraulic efficiency ηh = 92% = 0.92

Overall efficiency η0 = 84% = 0.84

Specific speed NS = 300

To find:

(1) Net head (H)

(2) Discharge (Q)

(3) Runner diameter (D0)

(4) Guide vane angle (α)

(5) Inlet vane angle (θ)

Solution:

Result:

1. Net head (H) = 32.93m

2. Discharge (Q) = 51.592 m3 / s 

3. Runner diameter (D0) = 2.038m 

4. Guide vane angle (α) = 51.95°

5. Inlet vane angle Q = 112.64°