Francis Turbine MCQ Quiz in বাংলা - Objective Question with Answer for Francis Turbine - বিনামূল্যে ডাউনলোড করুন [PDF]

Explanation:

According to the direction of flow through the runner, the turbine is classified as:

• Tangential flow turbines: In this type of turbines, the water strikes the runner in the direction of the tangent to the wheel. Example: Pelton wheel turbine
• Radial flow turbines: In this type of turbines, the water strikes in the radial direction. Accordingly, it is further classified as:
  • Inward flow turbine: The flow is inward from the periphery to the centre (centripetal type). Example: old Francis turbine.
  • Outward flow turbine: The flow is outward from the centre to the periphery (centrifugal type). Example: Fourneyron turbine.
• Axial flow turbine: The flow of water is in the direction parallel to the axis of the shaft. Example: Kaplan turbine and propeller turbine.
• Mixed flow turbine: The water enters the runner in the radial direction and leaves in an axial direction. Example: Modern Francis turbine

Explanation:

Speed ratio: 

• It is defined as the ratio of tangential velocity or circumferential velocity to its spout velocity and denoted b.
• ϕ = \(\frac{U_1{}}{\sqrt{2gH}}\) Where, U1 = Tangential velocity, \({\sqrt{2gH}}\) = Spout velocity
• Speed ratio varies from ie 0.6 ≤  ϕ ≤ 0.9

Flow ratio:

• It is defined as the ratio of flow velocity at the inlet to the spout velocity.
•  ψ = \(\frac{V_{f1}}{\sqrt{2gH}}\) Where, Vf1 = Flow velocity at inlet and \({\sqrt{2gH}}\) = Spout velocity.
• Flow value varies from ie 0.15 ≤ ψ ≤ 0.3

Additional Information 

Concept:

Specific speed of the turbine (NS)

NS = \(\frac{{{\rm{N}}\sqrt {\rm{P}} }}{{{{\rm{H}}^{5/4}}}}\)

P → shaft power = 100 kW

H → Head = 1 m

N → Speed = 10 rpm

Calculation:

NS = \(\frac{{{\rm{N}}\sqrt {\rm{P}} }}{{{{\rm{H}}^{5/4}}}}\)

NS = \(\frac{{10{\rm{\;}} × {\rm{\;}}\sqrt {100} }}{{{{\left( {1} \right)}^{5/4}}}}\)

NS = 10 × 10 = 100

Explanation:

According to the direction of flow through the runner, the turbine is classified as:

• Mixed flow turbine: The water enters the runner in the radial direction and leaves in an axial direction. Example: Modern Francis turbine
• Tangential flow turbines: In this type of turbine, the water strikes the runner in the direction of the tangent to the wheel. Example: Pelton wheel turbine
• Radial flow turbines: In this type of turbine, the water strikes in the radial direction. Accordingly, it is further classified as:
  • Inward flow turbine: The flow is inward from the periphery to the center (centripetal type). Example: old Francis turbine.
  • Outward flow turbine: The flow is outward from the center to the periphery (centrifugal type). Example: Fourneyron turbine.
• Axial flow turbine: The flow of water is in the direction parallel to the axis of the shaft. Example: Kaplan turbine and propeller turbine.

Explanation:

Classification of the turbine based on the energy available at the inlet:

i) Reaction Turbine: A turbine for which both pressure energy and kinetic energy is available at the inlet is a reaction turbine.

E.g. Francis Turbine, Kaplan Turbine, and Propeller Turbine.

They are useful for low head and high discharge.

ii) Impulse Turbine: A turbine for which only kinetic energy is available at the inlet is an impulse turbine.

E.g. Pelton Turbine and Turgo Impulse Turbine.

They are useful for high head and low discharge.

Concept:

Power developed in a reaction turbine is given by:

\(P = \;\frac{{\rho QgH{\eta _o}}}{{1000}}\)

Where,

ρ = density of the water (kg/m³)

Q = Discharge through the turbine (m³/s)

H = Head (m)

η_o = the overall efficiency of the turbine 

Calculation:

ρ = 1000 kg/m³

Q = 35 m3/sec

H = 9 m

\(P = \;\frac{{1000 \times 35 \times 9.81 \times 9 \times 0.91}}{{1000}}\)

P = 2812.036 kW

Concept:

The type of turbine to be used can be determined from the specific speed of a turbine.

Specific speed of a turbine \(\left( {{N_S}} \right) = \frac{{N\sqrt P }}{{{{\left( H \right)}^{5/4}}}}\)

Where, N = speed in RPM, P = power (in kW) and H = Head (in m)

Calculation:

N = 100

P = 6000

H = 25 m

\({N_S} = \frac{{100\; \times \;\sqrt {6000} }}{{{{\left( {25} \right)}^{5/4}}}} = 138.56\)

As the specific speed is in the range of specific speed of a Francis turbine.

So Francis turbine should be used.

Explanation:

Unit Quantities:

If the speed, discharge, and power developed by a turbine under a head are known, then by using unit quantities the speed, discharge, and power developed by the same turbine under a different head can be obtained easily.

They are as follows:

\(N_u=\frac{N_1}{\sqrt{H_1}}=\frac{N_2}{\sqrt{H_2}}\)

\(Q_u=\frac{Q_1}{\sqrt{H_1}}=\frac{Q_2}{\sqrt{H_2}}\)

\(P_u=\frac{P_1}{{H_1^{3/2}}}=\frac{P_2}{{H_2}^{3/2}}\)

Explanation:

In Francis turbine, discharge is radial at the outlet and hence whirl velocity (Tangential component of absolute velocity) at the outlet is zero.

Explanation:

Speed ratio: 

• It is defined as the ratio of tangential velocity or circumferential velocity to its spout velocity and denoted b.
• ϕ = \(\frac{U_1{}}{\sqrt{2gH}}\) Where, U1 = Tangential velocity, \({\sqrt{2gH}}\) = Spout velocity
• Speed ratio varies from ie 0.6 ≤  ϕ ≤ 0.9

Flow ratio:

• It is defined as the ratio of flow velocity at the inlet to the spout velocity.
•  ψ = \(\frac{V_{f1}}{\sqrt{2gH}}\) Where, Vf1 = Flow velocity at inlet and \({\sqrt{2gH}}\) = Spout velocity.
• Flow value varies from ie 0.15 ≤ ψ ≤ 0.3

Calculation:

Given:

ϕ₁ = 0.8, ϕ₂ = 0.6, H₁ = H₂ = H = 150 m

ϕ = \(\rm \dfrac{U{}}{\sqrt{2gH}}\) 

∴ \(\rm \dfrac{ϕ _1}{U_1} = \dfrac{ϕ _2}{U_2}\)       [∵ \(\rm \sqrt{2gH_1} = \sqrt{2gH_2}\) ]

∴ ϕ₁ U₂ =  ϕ₂U₁                   

0.8 × U2 =  0.6 × U1

\(\rm \dfrac{U_2}{U_1} = \dfrac{0.6}{0.8} = \dfrac{6}{8} = \dfrac{3}{4}\)