Pelton Wheel Turbine MCQ Quiz in తెలుగు - Objective Question with Answer for Pelton Wheel Turbine - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Concept:

The velocity diagram of a Pelton wheel is given below -

V₁, V₂ = Velocity of the jet at inlet and outlet.

u₁, u₂ = Velocity of the vane at inlet and outlet.

V_r1, V_r2 = Relative velocity of jet at inlet and outlet.

V_w1, V_w2 = Whirl velocity i.e. component of velocity parallel to the direction of motion.

V_f1, V_f2 = Flow velocity i.e component of velocity perpendicular to the direction of motion.

α = ∠ between the direction of jet and direction of motion.

θ = ∠ between V_r1 and the direction of motion.

β = ∠ between V₂ with the direction of motion.

ϕ = ∠ between V_r2 with the direction of motion.

Hydraulic efficiency is given by - 

\(η_h=\frac{R.P}{W.P}=\frac{\rho{Q}[V_{w1}\;\pm\;{V_{w2}}]u}{\rho{Q}gH}\)

Calculation:

Given:

For Pelton wheel 

V₁ = V_w1, u₁ = u₂ = u, V_r1 = V_r2.

If Nozzle is 100 % efficient -

\(⇒\rho{Q}gH=\frac{1}{2}\dot{m}{V_1}^{2}\)

Hydraulic efficiency is:

\(η_h=\frac{R.P}{W.P}=\frac{\rho{Q}[V_{w1}\;\pm\;{V_{w2}}]u}{\rho{Q}gH}\)

∴ \(η_h=\frac{\rho{Q}[V_{w1}\;\pm\;{V_{w2}}]u}{\frac{1}{2}\dot{m}{V_1}^{2}}\)

\(⇒ η_h=\frac{2[V_{w1}\;\pm\;{V_{w2}}]u}{{V_1}^{2}}\)   \([∵ \dot{m}=\rho{Q}]\)

V_w2 = V_r2cos ϕ - u

⇒ V_w2 = V_r1cos ϕ - u  (∵ V_r1 = V_r2)

⇒ V_w2 =  (V_w1 - u)cos ϕ -u (∵ V_r1 = V_w1 - u)

\(η_h=\frac{2[V_{w1}\;\pm\;{V_{w2}}]u}{{V_1}^{2}}\)

\( ⇒ {η _h} = \frac{{2\left[ {{V_1} + \left( {{V_1} - u} \right)\cos \phi - u} \right]u}}{{V_1^2}}\;\;\;[\because V_{w1}=V_{1}]\)

\( ⇒ \frac{{2u\left( {{V_1} - u} \right)\left[ {1 + \cos \phi } \right]}}{{V_1^2}}\)

For η_h to be maximum; \(\frac{d\eta_{h}}{du}=0\)

\(\frac{d\eta_{h}}{du}= 2(V_{1}-u)+2u(-1)\)

∴ 2u = 2V₁ - 2u

⇒ 4u = 2V₁

∴  \(\frac{u}{V_{1}} = \frac{{1}}{2}\Rightarrow 0.5\)

Concept:

The three hydraulic turbins can be divided based upon head and flow rate (discharge). This is shown below.

Calculation:

Based upon above table, descending order of flow rate/discharge will be;

Kaplan > Francis > Pelton ⇒ option A) is correct

Keypoints:

If descending order of available head had been asked, then answer would be;

Explanation:

Design parameters of the Pelton wheel turbine:

1. Velocity of jet: at inlet \({V_1} = {C_V}\sqrt {2gH} \) where Cv = coefficient of velocity = 0.98-0.99
2. The velocity of wheel: \(u = \emptyset \sqrt {2gH} \) where φ is the speed ratio = 0.43-0.48
3. The angle of deflection: is 165° unless mentioned.
4. Pitch or mean diameter: D can be expressed by \(u = \frac{{\pi DN}}{{60}}\)
5. Jet ratio: \(m = \frac{D}{d}\) (12 in most cases/calculate), d = nozzle diameter or jet diameter
6. Number of buckets on a runner: \(Z = 15 + \frac{D}{{2d}}\) (Tygun formula) or, \(Z = 5.4\sqrt m\), m = 6 to 35
7. Number of Jets: obtained by dividing the total rate of flow through the turbine by the rate of flow through single jet. The number of jets is not more than two for horizontal shaft turbines and is limited to six for vertical shaft turbines.
8. Size of bucket: length of bucket L = 2.5d, width of bucket B = 5d, depth of bucket Db = 0.8d

Concept:

The overall efficiency of the Pelton wheel is given by,

\({η _o} = \frac{{Shaft \;Power}}{{Water\; Power}}\)

Water Power = ρ × g × Q × H 

Calculation:

Given:

Shaft Power = 800 kW, η_o = 0.8, H = 50 m

Water Power = γ × Q × H = 10000 × Q × 50 = 500000Q 

\({η _o} = \frac{{Shaft \;Power}}{{Water\; Power}}= \frac{800 \times 1000}{500000Q}= 0.8\)

Q = 2m³

The flow rate is 2 m³

Concept:

Pelton wheel turbine:

• A Pelton wheel turbine is a tangential flow impulse turbine.
• In an impulse turbine total energy at the time of inlet of the turbine is only kinetic energy.
• A Pelton wheel turbine is used for the high head of water.
• The pressure of water both at entering and leaving the vanes is atmospheric.

Explanation:

From the above diagram, the correct sequence of energy conversion starting from the entry of the fluid is Potential energy - Kinetic Energy - Mechanical energy. 

∴ The correct sequence is Potential energy - Kinetic Energy - Mechanical energy. 

Explanation:

Number of buckets on a runner: \(Z = 15 + \frac{D}{{2d}}\) 

Calculation:

Given:

Jet ratio = 8 i.e D/d = 8

Now,

Number of buckets on a runner = 15 + 4 = 19

∴ Number of buckets = 19

Important Points

Design parameters of Pelton wheel turbine:

1. 1Velocity of jet: at inlet \({V_1} = {C_V}\sqrt {2gH} \) where Cv = coefficient of velocity = 0.98-0.99
2. 2Velocity of wheel: \(u = \emptyset \sqrt {2gH} \) where φ is the speed ratio = 0.43-0.48
3. 3Angle of deflection: is 165° unless mentioned.
4. 4Pitch or mean diameter: D can be expressed by \(u = \frac{{\pi DN}}{{60}}\)
5. 5Jet ratio: \(m = \frac{D}{d}\) (12 in most cases/calculate), d = nozzle diameter or jet diameter
6. Number of buckets on a runner: \(Z = 15 + \frac{D}{{2d}}\) (Tygun formula) or, \(Z = 5.4\sqrt m \), m = 6 to 35
7. Number of Jets: obtained by dividing the total rate of flow through the turbine by the rate of flow through single jet. The number of jets is not more than two for horizontal shaft turbines and is limited to six for vertical shaft turbines.
8. Size of bucket: length of bucket L = 2.5d, width of bucket B = 5d, depth of bucket Db = 0.8d 

Concept:

Pelton Wheel Turbines:

• Pelton wheel turbine is a tangential flow, high head impulse turbine. 
• Pelton wheel is for the head of more than 100 m 
• In this turbine, a water jet impinges on the bucket attached to the shaft of the turbine which causes a force on the bucket.
• This force creates torque necessary for the rotation of the shaft.
• All the head is converted to the kinetic head before the jet impinges on the bucket.
• While moving on the bucket, water is always in contact with the atmosphere. Hence throughout its operation water is atmospheric pressure.

The Main Parts of Pelton Turbine are:

Explanation: 

Pelton wheel or turbine

It is a tangential flow impulse turbine. The water strikes the bucket along the tangent of the runner. The energy available at the inlet of the turbine is kinetic energy. The pressure at the inlet and outlet of the turbine is the atmosphere. This turbine is used for high head and low discharge.

The main parts of Pelton wheel are:

• Nozzle and flow regulating arrangement.
• Runners and buckets.
• Casing
• Breaking jet
  When the nozzle is completely closed by moving the spear in the forward direction, the amount of water striking the runner reduces to zero. But the runner due to inertia goes on revolving for a long time. To stop the runner in a short time, a small nozzle is provided which directs the jet of water on the back of the vanes. This jet of water is called a breaking jet.

• The speed ratio of the Pelton wheel varies between 0.45 to 0.50.
• The value of the jet ratio is generally taken as 12.
• Number of buckets Z, can be found from simple relation, Z = 15 + 0.5m.​

Concept:

Classification of the turbine are as follows:

1. According to the type of energy at Inlet

a) Impulse Turbine - Pelton Wheel (Requires High Head and Low Rate of Flow)

b) Reaction Turbine - Francis, Kaplan (Requires Low Head and High Rate of Flow)

2. According to the direction of flow through runner

a) Tangential Flow Turbine - Pelton Wheel

b) Radial Flow Turbine - Francis Turbine

c) Axial Flow Turbine - Kaplan Turbine

d) Mixed Flow Turbine - Modern Francis Turbine

3. According to Head at Inlet of turbine

a) High Head Turbine - Pelton Wheel

b) Medium Head Turbine - Francis Turbine

c) Low Head Turbine - Kaplan Turbine

4. According to Specific Speed of Turbine

a) Low Specific Speed Turbine - Pelton Wheel

b) Medium Specific Speed Turbine -Francis Turbine

c) High Specific Speed Turbine - Kaplan Turbine

5. According to Disposition of Turbine Shaft

a) Horizontal Shaft - Pelton Wheel

b) Vertical Shaft - Francis & Kaplan Turbines

Explanation:

Pelton wheel or turbine:

• It is a tangential flow impulse turbine. The water strikes the bucket along the tangent of the runner.
• The energy available at the inlet of the turbine is kinetic energy. The pressure at the inlet and outlet of the turbine is the atmosphere.
• This turbine is used for high head and low discharge.
• Jet ratio = \(\frac{Diameter\;of\;wheel }{Jet\; diameter}\)
• A jet ratio of 12 is normally adopted

​
The main parts of the Pelton wheel are:

• Nozzle and flow regulating arrangement.
• Runners and buckets.
• Casing
• Breaking jet
• When the nozzle is completely closed by moving the spear in the forward direction, the amount of water striking the runner reduces to zero. But the runner due to inertia goes on revolving for a long time. To stop the runner in a short time, a small nozzle is provided which directs the jet of water on the back of the vanes. This jet of water is called a breaking jet.

​

Important Points ​

• Nozzle efficiency = \(\frac{K.E\;of\;jet\;per\;second}{Water\;power\;at\;the\;base\;of\;nozzle}\)
• Hydraulic efficiency = \(\frac{Runner\;power}{Kinetic\;energy\;per\;second}\)
• η_{max. hydraulic} = \(\left( {\frac{{1 + k\cos \phi }}{2}} \right)\), k = friction factor for blades
• Overall efficiency = η_o × η_nozzle × η_hyd × η_mech
• Coefficient of velocity = C_v = 0.97 - 0.99
• speed ratio = 0.43 - 0.47
• No. of buckets (z) = \(\frac{D}{2d}\) + 15 = 18 to 25