FIGURE 2.15: Fans installed in parallel
PROBLEM SET:
1. The power output of a fan is 120 kW with efficiency of 80%. Determine the horsepower output required by the motor to drive the fan. (Ans. 201 hp)
2. The static head of a fan is measured to be 160 mm of water gage at an air velocity of 25 m/s. Find the air power at an air condition of 28°C and 98 kPa with a volume flow rate of 5 m3/s. (Ans. 9.6 kW) 3. Determine the horsepower required for a fan delivering 35 ft/sec of air through a 2.3 ft x 3.5 ft duct
with a total pressure of 3.5 in water gage. Take density of air to be 0.075 lb/ft3. (Ans. 9.3 hp) 4. A fan operating at a standard air condition registered a total static head of 230 mm of water gage.
If the static efficiency is 65% and the fan efficiency is 80% determined the velocity of air if the volume of air delivered is 6 m3/s. (Let the velocity head to be 35% of the static head). (Ans. 34.6 m/s) 5. A fan initially operating at a speed of 380 rpm at an air temperature of 26°C. If the speed is increased
to 460 rpm with 55°C, determine the new head in mm of water gage for an initial head 190 mm of water gauge. (Ans. 253.8 mm)
6. What is the horsepower required for a fan to deliver 230 ft3/sec of air through a 2.5 ft x 4.5 ft duct under a total pressure of 4.2-in water gage? (Ans. 0.35 hp)
7. The rating of a fan is 610 m3/min when running at 360 rpm and requires 8 kW motor to drive it. If the fan speed is increased to 620 rpm and the air handled becomes 60°C instead of 30°C, determine the power in kW. (Ans. 37.1 kW)
8. A fan has a static head of 110 m at a pressure of 1.5 kg/cm2 and 75°F. If the air velocity is 18 m/s, determine the total equivalent head in mm of water gage. (Ans. 145.61 mmWG)
HYDRAULIC TURBINES
Fluid machines are those machines which are used to convert mechanical energy into fluid energy or vice versa. Machines that coverts fluid energy into mechanical energy are known as turbines.
Machines that converts mechanical energy into fluid energy are known as pumps.
Water turbines. Turbines are devices to convert energy of water into mechanical energy which can be used for running electricity generators.
Types of Hydraulic Turbines 1) Reaction turbines
2) Impulse turbines
In reaction turbines, pressure head of water is converted into velocity head as water flows through the turbine. Reaction turbines run full of water and hence the turbine maybe entirely submerged below the tail race or may discharged into the atmosphere. It may also discharge into a suction or draught tube when placed 9.14 m above the foot of fall. In these turbines water must enter over the whole circumference.
In impulse turbine, the energy of water is converted into velocity before entering the wheel at atmospheric pressure and this will not permit the turbine tube to be flooded. The water is passed through nozzle or guide vanes for converting all its energy into velocity. Impulse turbine must be placed at the foot and above the tail race. Hence these turbines can be inspected easily. The water maybe entered over entire circumference or part of the circumference.
If H is the head at which water is available and leaves the turbine at velocity V1, then the energy available from turbine or energy of water absorbed by turbine will be;
H = 𝑉2𝑔12
However, the impulse turbine, this energy H will first be converted into velocity or kinetic energy at velocity V.
Both reaction and impulse turbines can be further classified depending upon direction of flow. The flow is axial in axial flow turbines and radial and radial flow turbines. Mixed flow turbines are also in used. The radial flow turbine may have flow from centre to circumference or vice-versa.
Commonly used turbines are:
a) Kaplan turbine/Propeller type, reaction turbine suitable for very low heads.
b) Francis turbine. A reaction turbine suitable for medium heads.
c) Pelton wheel. An axial flow impulse turbine for high heads d) Turgo wheel. An impulse turbine suitable for medium heads.
In an inward radial flow turbine fixed guide blades surround the revolving blades externally whereas in an outward flow turbine the ring of moving blades surrounds the fixed guide blades The water leaves through the centre in latter case while it enters the turbine though centre in former. In outward flow turbine the relative velocity of water is increased and hence quantity of water passing through the turbine is increased. This tendency would not exists in inward flow turbines. In fact, this case may increase the speed of the wheel will tend to decrease the flow through the wheel and reduce power.
In axial flow turbine, the guide blade and rotating blade rings are mounted side by side and water flows from guide blades into moving blades parallel to the axis of turbine. For this reason the turbines are called parallel flow.
Types of Hydraulic turbines
1.0)Impulse turbine also known as Tangential wheel or Pelton wheel It is a Pressureless Turbine
__ a turbine that utilizes kinetic energy of high velocity jet which acts upon a small part of the circumference at an instant.
__ Movement of the water is tangential
__ Suited for very high heads plants (150 m and above) and low volume of water __ No exact value for critical head, hence heads are given in range
__Impulse turbine has no draft tube
__ Typical turbine efficiencies are in the range of 80% to 90%
__Higher efficiencies are associated with turbines having two or more runners.
2.0) Reaction Turbines (Francis type or Propeller type). It is Pressure Turbine
__ a turbine which develops power from the combined action of pressure and velocity of water that completely fills the runner and the water passages
__Movement of water for reaction turbines can be radial for Francis type and axial for Propeller/Kaplan type __Reaction turbine has draft tube which keeps the turbine up to 5m( 15 ft) above the tail water
__Reaction turbine conversion efficiency is usually higher than that of Impulse turbine __Reaction turbines’ conversion efficiency is about 85% to 95%
Turbine type recommended based on head Net head Type of turbine
Up to 70 ft Propeller type
70 to 110 ft Propeller or Francis type
110 to 800ft Francis type
800 to 1300 ft Francis type or Impulse type 1300 and above Impulse type
Types of reaction turbines
A. Francis Type--- for medium head
B. Propeller and Kaplan type Reaction turbine for very low head
Propeller has fixed blade. A type of reaction turbine with reduced number of fixed blades. The flow is axial. Suited for low head plant and has usual conversion efficiency of 80%
Kaplan type has adjustable blades. The flow is inward flow axial. Suited for low headed and large volum e of water and usual conversion efficiency of more or less than 93%.
Performance of Hydroelectric Power Plant
1. Gross head, hg---- is the difference between water and tail water elevations . hg= hhw - htw
where: hhw =headwater elevation htw = tail water elevation 2. Friction head loss,hf
Friction head loss- is the head lost by the flow in a stream or conduit due to frictional disturbances set up by the moving fluid and its containing conduit and by intermolecular friction.
Using Darcy equation hf=𝑓𝐿𝑉2
2𝑔𝐷
Using Morse equation hf = 2𝑓𝐿𝑉2
𝑔𝐷
where: hf= friction head in meter f = coefficient of friction L = total length in m
g = 9.81 m/s2
D= inside diameter in m
Note: Friction head loss is usually expressed as a percentage of the gross head
3. Net head or Effective head is the difference between the gross head and the friction head loss H = hg-hf
4. Penstock efficiency is the ratio of the net head to the gross head ep = ℎ𝑔ℎ
5. Volume flow rate of water, Q –it is the product of the velocity and the cross-sectional area.
Q=AV
6. Water Power- is the power generated from an elevated water supply by the use of hydraulic turbines 7. Turbine efficiency—is the ratio of turbine power output to the water power output
et = 𝑇𝑢𝑟𝑏𝑖𝑛𝑒 𝑃𝑜𝑤𝑒𝑟
𝑊𝑎𝑡𝑒𝑟 𝑃𝑜𝑤𝑒𝑟 = 𝑃𝑤𝑃𝑡, and Pt = ɤQhet
8. Electrical or generator efficiency is the ratio of the generator output to the turbine power output eG = 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝑜𝑢𝑡𝑝𝑢𝑡
𝑇𝑢𝑟𝑏𝑖𝑛𝑒 𝑜𝑢𝑡𝑝𝑢𝑡 =𝑃𝑔𝑒𝑛
𝑃𝑡 ; Pgen =Ptegen = ɤQhetegen
9. Generator Speed, N =120𝑓𝑃 , where: N= angular frequency, rpm F= frequency (usually 60 hertz), P = no. of poles,(even number) 10. Head of impulse turbine
h =𝑃ɤ + 𝑉2𝑔2’ meters of water 11. Head of reaction turbine
H= 𝑃ɤ + Z +𝑉𝐴22𝑔−𝑉𝐵2 12. Peripheral coefficient
It is a ratio of the peripheral velocity(Vp) to the velocity of the jet (Vj) 𝟇 = 𝜋𝐷𝑁
√2𝑔ℎ where: D= diameter of the runner N= angular speed, h= net head
13. Specific speed-is a number used to predict the performance of the hydraulic turbines a) In English units
14. Hydraulic efficiency is the ratio of the utilized head to the net head Eh = ℎ𝑤ℎ
Components Parts of a water turbine
A. Wheel- commonly known as runner, it is along with the vanes on its periphery, rotates under the action of water gliding on the vanes comes from the gliding apparatus.
B. Guiding Apparatus (or mechanism), which guides the water to the vanes of runner.
C. In addition, there will be a source of supply from which water will come through a pipe line ( known as penstock) to the guiding mechanism also, there will be a tailrace in which the water, after gliding over the moving blades of the runner and passing out of runner, will ultimately fall from the turbine.
Classification of turbine according to the direction of flow A. Radially inward flow turbine
B. Radially outward flow turbine C. Axial flow turbine or parallel flow D. Mixed flow turbine
A turbine, whether Impulse or Reaction may have one of the following settings A. Vertical setting, B. Horizontal setting C. Above the tai race D. Below the tail race
A turbine is said to be vertical or with vertical setting when its shaft is vertical and its runner is horizontal, this arrangement gives better efficiency due to the reduced losses. This setting is usually used for reaction turbines, it may also used for pelton wheel having more than two nozzles.The vertical setting is said to be used for low heads.
A turbine is said to be horizontal or with horizontal setting when its shaft is horizontal and its runner is vertical. This setting is usually for Pelton wheel with one or two nozzles.
HEADS at Inlet and Outlet of Runner of Reaction Turbine
H=𝑤𝑃 + 𝑉2𝑔2, meters of water; Similarly, if V1 and P1 are respectively the velocity and intensity of pressure at the outlet of runner, the total head at outlet runner,
H1 =𝑃𝑤1 + 𝑉2𝑔2 meters of water; where: h= total head at inlet, in m; V= absolute velocity with which water from guide passages, enters the inlet of the runner, m/s; P= intensity of pressure at the inlet of the runner in kg/m2. Applying modified Bernoullis’ Theorem to the outlet of the horizontal runner.
H= h1+ total losses between inlet and outlet of the runner
= h1 + friction loss(hydraulic loss) in runner + head used due to the work done by water on runner. If hf be the loss of head in guide passages and Z be the elevation of inlet above the tail race, he total head H on turbine
H= hf + 𝑤𝑃 + 𝑉2𝑔2 + Z
Efficiency and horsepower of reaction turbine The efficiency of a turbine may be
a) Hydraulic efficiency, ɳh b) Mechanical efficiency,ɳm
c) Overall efficiency, ɳo
Hydraulic efficiency = ℎ𝑦𝑑𝑟𝑎𝑢𝑙𝑖𝑐 𝑜𝑢𝑡𝑝𝑢𝑡
ℎ𝑦𝑑𝑟𝑎𝑢𝑙𝑖𝑐 𝑖𝑛𝑝𝑢𝑡= 𝐻𝑃 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 𝑏𝑦 𝑤𝑎𝑡𝑒𝑟 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑢𝑛𝑛𝑒𝑟
𝑊𝐻 75
Where; 𝑊𝐻
75= horsepower of water on available water horsepower 75=1 metric horsepower, ℎ𝑝−𝑠𝑒𝑐𝑘𝑔−𝑚
Mechanical efficiency= 𝑊𝑜𝑟𝑘 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑠ℎ𝑎𝑓𝑡
1) Specific Speed of turbine- speed of an imaginary or specific turbine( which is a small model of the original turbine) which develops one SHP when working under a net head of one meter.
Discharge of turbine, Q= Area of flow times velocity of flow.= πDbVf; taking the turbine to be a reaction turbine , but;
U= tangential velocity =𝜋𝐷𝑁60 ; D=𝑈(60)𝜋𝑁 ; D∞𝑈𝑁, Speed ratio= 𝑈
√2𝑔𝐻 of a turbine is a certain constant, U= constant ( √2𝑔𝐻) : Constant =Cv= coefficient of velocity of nozzle
For a turbine, b =fD; therefore b∞√𝐻
𝑁
Ns=𝑁√𝑃
𝐻54
Equation for specific speed using 2 jet pelton wheel Ns2= 𝑁√2𝑃
𝐻54
3. Conditions of working of a Turbine 𝐷1𝑁1
A reaction turbine develops 500 BHP. Flow through the turbine is 50 cfs. Water enters at 20 fps with a 100 ft pressure head. The elevation of the turbine above the tail water level is 10 ft. Find the
Example #02
A proposed scheme has an available head of 480 m and the 3 single jet pelton wheels to be installed are required to run at 330 rpm. Assuming an over-all efficiency of 85%, determine the total quantity of water required per second. Assume that the specific speed of Pelton is 18.
Solution:
Determine the specific speed of a pelton wheel of which the basis design criteria are as follows:
Coefficient of velocity of nozzle, Cv= 0.98, runner velocity = 0.46 x jet velocity,
𝐽𝑒𝑡 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑟𝑢𝑛𝑛𝑒𝑟 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 =𝐷𝑚𝑒𝑎𝑛𝑑𝑐 = 101 Overall efficiency = 82%
Solution; for runner , tangential velocity, U= 𝜋𝐷𝑚𝑒𝑎𝑛𝑁60 eq. 1 Where: Dmean= effective runner diameter,m
N= speed of the runner, rpm U= tangential velocity, m/s
For water jet, absolute velocity or jet velocity= V= Cv √2𝑔𝐻----eq.2 Where Cv =coefficient of velocity of nozzle
H= net head of turbine,m
V= jet velocity m/s, But runner velocity, U=0.46 x V----eq.3 Substituting eq.1 and eq.2 to eq.3
𝜋𝐷𝑚𝑒𝑎𝑛 𝑁
Taking the square root of both sides SHP1/2 = [ 37.275 dc2 x H3/2]1/2