lab-x

CE 302 Laboratory #5 Turbine Efficiency Spring 2024

1

Objective: Determine the characteristic curve (i.e., peak efficiency vs. discharge) for a Pelton wheel turbine. This is performed by measuring the rotational speed of the turbine wheel and the break force applied to the wheel for three different flow rates at a constant head. In addition to the curve listed above three additional graphs will be constructed plotting angular velocity vs. torque, power-out, & efficiency for the three flow rates. A schematic of a typical Pelton wheel is given below. A total of four graphs will need to be created for this laboratory exercise.

Note: A total of 3 tables and 4 graphs will be drawn for this report.

A nozzle directs forceful, high-speed streams of water against a rotary series of spoon-shaped buckets which are mounted around the circumferential rim of a drive wheel. Water impulse energy exerts torque on the bucket-and-wheel systems spinning the wheel. In the process, the

The relationship between flow and efficiency (characteristic curve) is determined by measuring the hydraulic power of the water (including both the pressure and velocity head) and also by measuring the power generated by the turbine (from the braking force on the turbine and the rotational speed). By measuring the power input and output of the turbine, the overall efficiency is determined and the most effective operation for the turbine is identified.

As stated earlier the total head is the hydraulic head (pressure) plus the velocity head. In this system, the hydraulic head (h) is measured from the pressure generated by the pump and is held at a constant 55 ft. (16.764 m) The velocity head H) is measured by dividing the squared value of the approaching velocity of the water traveling through a 1-inch (0.0254 m) diameter pipe by twice the gravitational force of gravity. This equation is given as;

2/2g

Where H is velocity head (ft.), v is jet velocity (m/s), and g is gravitational force (m/s2).

CE 302 Laboratory #5 Turbine Efficiency Spring 2024

2

In order to measure the amount of energy converted from hydraulic to mechanical energy by the turbine, a breaking mechanism is attached to the shaft of the turbine. The brake force applied to the turbine is the force applied by the breaking mechanism to the rotating shaft of the turbine. This force is a friction force. The breaking force applied to the braking mechanism creates a torque on the rotating shaft. Torque is force times the distance away from the point of rotation. In the case for this lab the distance from the point of rotation (L) is a constant 0.16032 m (0.526 ft = 6.312 in) The Torque equation is given by;

T = F*L

The power input for the turbine is the power generated by the total head of the water in system. The velocity head and hydraulic head of the water make up the total head which makes up the power of the water. The power contained in the water is the input power which is calculated by multiplying the specific weight of water times the flow rate (Q) times the total head . The equation is given by;

Pin =

The power output is calculated by taking the breaking torque (T) times the angular speed of the turbine. The efficiency of the turbine is the ratio of the power output divided by the power input. The equations for each are given as;

Pout

In the laboratory experiment a To verify proper speed

3

Flow (cfm) = 6.7 Flow (m3/s) = 0.0032 Jet Velocity (m/s) = 6.24 Table 1

Angular Angular Brake Break Power Velocity Total Power Speed Speed Force Force Torque Out Head Head In Efficiency

(rpm) (rad/s) (lbf) (N) (Nm) (Nm/s) (m) (m) (Nm/s) (%) 2238 234.4 0 0.00 0 0 0 2146 224.7 0.7 3.11 0.50 112.18 19.3 2057 215.4 1.1 4.89 0.78 168.97 29.1 1919 201.0 1.7 7.56 1.21 243.62 42.0 1754 183.7 2.4 10.68 1.71 314.37 1.985 18.75 579.87 54.2 1512 158.3 3.2 14.23 2.28 361.32 62.3 1133 118.6 4.1 18.24 2.92 346.90 59.8

807 84.5 5.1 22.68 3.64 307.35 53.0 0 0.0 5.9 26.24 4.21 0.00 0.0

Flow (cfm) = 6.0 Flow (m3/s) = 0.0028 Jet Velocity (m/s) = 5.59 Table 2

Angular Angular Brake Break Power Velocity Total Power Speed Speed Force Force Torque Out Head Head In Efficiency

(rpm) (rad/s) (lbf) (N) (Nm) (Nm/s) (m) (m) (Nm/s) (%) 2220 232.5 0 0.00 0 0 0.0 2150 225.1 0.6 2.67 0.43 96.34 18.9 2020 211.5 1.1 4.89 0.78 165.94 1.592 18.36 508.40 32.6 1849 193.6 1.6 7.12 1.14 220.93 43.5 1420 148.7 2.5 11.12 1.78 265.11 52.1

0 0.0 5 22.24 3.57 0.00 0.0

Results

4

Flow (cfm) = 4.4 Flow (m3/s) = 0.0021 Jet Velocity (m/s) = 4.10 Table 3

Angular Angular Brake Break Power Velocity Total Power Speed Speed Force Force Torque Out Head Head In Efficiency

(rpm) (rad/s) (lbf) (N) (Nm) (Nm/s) (m) (m) (Nm/s) (%) 2183 228.6 0 0.00 0 0 0.0 2067 216.5 0.6 2.67 0.43 92.62 25.9 1775 185.9 1.3 5.78 0.93 172.32 0.856 17.62 357.88 48.2 1390 145.6 2 8.90 1.43 207.61 58.0 1000 104.7 2.6 11.56 1.85 194.16 54.3

0 0.0 3.7 16.46 2.64 0.00 0.0 Sample Calculations. Example calculations are for the following conditions (Table 1): Flow = 6.7 cfs (0.0032 m3/s) Angular speed = 2146 rpm Brake force = 0.7 lbf

Pipe area = 0.0005067 m2

Flow rate = 0.0032

Jet Velocity (V) = Q/A = 0.0032 / 0.0005067 m2 = 6.24

= 2146 rpm * = 224.7 rad/s

Brake Force (F) = 0.7 lbf * 4.448 = 3.11 N

Torque (T) = F*L = 3.11 N * 0.16032 m = 0.5 Nm

Power out (Pout = 112.8

= 1.985 m

= 16.764 m + 1.985 m = 18.75 m

Power in (Pin * (0.0032 ) * (18.75 m) = 579.87

Efficiency = * 100 = 19.3%

5

The data is then represented in the construction of 4 graphs. They are Torque vs Angular Speed, Power-Out vs. Angular Speed, Efficiency vs. Angular Speed, and Peak Efficiency vs. Flow rate. The graphs are presented below;

0

0.5

1

1.5

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2.5

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3.5

4

4.5

0 500 1000 1500 2000 2500

To rq

ue (N

m )

Angular Speed (rpm)

Torque vs. Angular Speed

Flow 6.7 cfm (0.0032 cm/s)

Flow 6.0 cfm (0.0028 cm/s)

Flow 4.4 cfm (0.0021 cm/s)

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50

100

150

200

250

300

350

400

0 500 1000 1500 2000 2500

Po w

er -O

ut (N

m /s

)

Angular Speed (rpm)

Power-Out vs. Angular Speed

Flow 6.7 cfm (0.0032 cm/s)

Flow 6.0 cfm (0.0028 cm/s)

Flow 4.4 cfm (0.0021 cm/s)

CE 302 Laboratory #5 Turbine Efficiency Spring 2024

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0

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0 500 1000 1500 2000 2500

Ef fic

ie nc

y (%

)

Angular Speed (rpm)

Efficiency vs. Angular Speed

Flow 6.7 cfm (0.0032 cm/s)

Flow 6.0 cfm (0.0028 cm/s)

Flow 4.4 cfm (0.0021 cm/s)

50

52

54

56

58

60

62

64

0.0015 0.0017 0.0019 0.0021 0.0023 0.0025 0.0027 0.0029 0.0031 0.0033

Pe ak

E ff

ic ie

nc y

(% )

Flow (m3/s)

Peak Efficiency vs. Flow