← Fluid Mechanics & Hydraulics · NTPC NGEL Engineer Civil

Chapter 12 of 12

Pumps & Turbines

In the NTPC NGEL Engineer Civil syllabus under Fluid Mechanics & Hydraulics · 2 parts

Hydraulic Turbines · Centrifugal & Reciprocating Pumps

CIVILGYAN TEST SERIES · civilgyantests.com — free study notes for civil engineering exams

📑 Contents (20 sections)

Part 1 of 2

Hydraulic Turbines

Last reviewed 16 Sept 2026 · 8 min read

Hydroelectric power plant

Water from a reservoir (behind a dam) flows through penstocks to turbines in the power house, then leaves through the tailrace. The turbine shaft drives a generator. A surge tank protects long conduits against water hammer (see Water Hammer & Surge Tanks).

Gross head $H_{g}$ — difference between headrace (reservoir) and tailrace levels.
Net (effective) head $H = H_{g} - h_{f}$ (friction loss in the penstock); for a Pelton wheel $H$ is measured at the nozzle base.

Efficiencies

Efficiency	Definition
Hydraulic $η_{h}$	Power delivered to the runner ÷ water power supplied $= \frac{runner power}{ρ g Q H}$
Mechanical $η_{m}$	Shaft power ÷ runner power
Volumetric $η_{v}$	Water actually striking the runner ÷ water supplied
Overall $η_{o}$	Shaft power ÷ water power $= η_{h} \times η_{m}$ (× $η_{v}$ if considered)

Water power $= ρ g Q H$ (W); shaft power $P = η_{o} ρ g Q H$ .

Classification of turbines

Basis	Types
Energy at inlet	Impulse — all available head converted to kinetic energy in a nozzle; runner at atmospheric pressure (Pelton). Reaction — water enters with both pressure and kinetic energy; runner is enclosed and runs full (Francis, Kaplan)
Direction of flow through runner	Tangential (Pelton), radial (old inward-flow Francis), mixed (modern Francis), axial (Kaplan, propeller)
Head (typical, overlapping)	High head (about 250 m and above) — Pelton; medium head (about 60–250 m) — Francis; low head (below about 60 m) — Kaplan/propeller
Specific speed	Low — Pelton; medium — Francis; high — Kaplan

Pelton wheel (impulse turbine)

Main parts: nozzle with spear (flow regulation), runner with double-hemispherical (split) buckets — the central splitter divides the jet — casing (prevents splashing; no hydraulic function), deflector (breaks the jet on sudden load rejection), braking jet.

FormulaPelton wheel relations

Jet velocity: $V_{1} = C_{v} 2 g H$ , $C_{v}$ ≈ 0.97–0.99
Bucket velocity: $u = ϕ 2 g H$ with speed ratio $ϕ$ ≈ 0.43–0.47; $u = \frac{π D N}{60}$
Work done per second (bucket friction factor $k$ , outlet blade angle $β$ , i.e. deflection $180° - β$ ):

P_{r u nn er} = ρ a V_{1} (V_{1} - u) (1 + k cos β) u

Hydraulic efficiency (based on jet kinetic energy $V_{1}^{2} /2 g$ ; multiply by $C_{v}^{2}$ to refer it to the net head):

η_{h} = \frac{2 ( V _{1} - u ) ( 1 + k cos β ) u}{V _{1}^{2}}

Maximum hydraulic efficiency when $u = V_{1} /2$ : $η_{h, ma x} = \frac{1 + k cos β}{2}$ (→ 100% if $β$ = 0 and $k$ = 1)
Jet ratio $m = D / d$ (wheel pitch-circle diameter ÷ jet diameter), usually about 11–14 (not less than about 6)
Number of buckets: $Z = 15 + \frac{m}{2}$ (empirical)

Buckets deflect the jet through about 160–165° (not 180°, so the leaving water does not strike the next bucket).

Francis turbine (inward mixed-flow reaction turbine)

Main parts: spiral (scroll) casing — cross-section decreasing to keep velocity uniform; stay vanes; guide vanes (wicket gates) — adjustable, regulate flow and set the inlet angle; runner with fixed curved vanes; draft tube.

FormulaFrancis turbine relations

Work done per second per unit weight: $\frac{V _{w 1} u _{1} \pm V _{w 2} u _{2}}{g}$
For radial (or axial) discharge at outlet ( $V_{w 2}$ = 0, best design): $η_{h} = \frac{V _{w 1} u _{1}}{g H}$
Discharge: $Q = π D_{1} B_{1} V_{f 1} = π D_{2} B_{2} V_{f 2}$ (vane thickness neglected)
Typical ratios: speed ratio $u_{1} / 2 g H$ ≈ 0.6–0.9; flow ratio $V_{f 1} / 2 g H$ ≈ 0.15–0.30; $B_{1} / D_{1}$ ≈ 0.1–0.45

Kaplan and propeller turbines (axial-flow reaction)

Water flows parallel to the shaft; the runner has few (usually 3–8) blades on a large hub (boss).
Propeller turbine — fixed blades; efficiency drops sharply at part load.
Kaplan turbine — adjustable runner blades (and adjustable guide vanes: "double regulated") — high efficiency over a wide load range.
Flow area: $Q = \frac{π}{4} (D_{o}^{2} - D_{b}^{2}) V_{f}$ ( $D_{o}$ outer, $D_{b}$ hub diameter); peripheral velocity at inlet and outlet is equal at any radius.
Suited to low heads and large discharges (river-bed plants, barrages).

Part 2 of 2

Centrifugal & Reciprocating Pumps

Last reviewed 16 Sept 2026 · 9 min read

Pumps

A pump converts mechanical energy into hydraulic (pressure) energy to lift liquid or move it through pipes.

Rotodynamic pumps — energy imparted by a rotating impeller (centrifugal, mixed-flow, axial-flow).
Positive displacement pumps — liquid trapped and forced out (reciprocating, gear, screw).

Centrifugal pump

Main parts

Impeller — rotating wheel with backward-curved vanes; types: closed (shrouds on both sides, clean water), semi-open and open (for sewage and solids).
Casing — airtight passage that converts kinetic energy to pressure:
- Volute casing — spiral of increasing area; simple, some eddy losses.
- Vortex casing — a circular chamber between impeller and volute; reduces eddy losses.
- Casing with guide blades (diffuser) — fixed diffuser vanes; highest efficiency (turbine pump).
Suction pipe with foot valve (non-return) and strainer at its lower end.
Delivery pipe with a delivery valve to regulate flow.

Priming — filling the suction pipe, casing and part of the delivery pipe with liquid before starting, to expel air. A centrifugal pump running in air develops negligible head (head ∝ density), so without priming it cannot lift water.

The pump is started with the delivery valve closed (power at shut-off is minimum for radial-flow pumps), then the valve is opened gradually.

Heads

Head	Definition
Suction head $h_{s}$	Height of pump centre above the sump water level
Delivery head $h_{d}$	Height of delivery outlet above the pump centre
Static head $H_{s}$	$h_{s} + h_{d}$
Manometric head $H_{m}$	Head actually imparted to the liquid: $H_{m} = h_{s} + h_{d} + h_{f s} + h_{f d} + \frac{V _{d}^{2}}{2 g}$ ; also = difference of pressure heads measured at outlet and inlet (+ velocity and datum corrections)
Euler (theoretical) head	$\frac{V _{w 2} u _{2}}{g}$ for radial entry ( $V_{w 1}$ = 0)

Efficiencies

Manometric efficiency: $η_{man} = \frac{g H _{m}}{V _{w 2} u _{2}}$
Mechanical efficiency: $η_{m}$ = power at impeller ÷ shaft power
Overall efficiency: $η_{o} = \frac{ρ g Q H _{m}}{shaft power} = η_{man} \times η_{m}$

Velocity triangles and work done

FormulaCentrifugal pump

Blade velocities: $u_{1} = \frac{π D _{1} N}{60}$ , $u_{2} = \frac{π D _{2} N}{60}$
Work done per second per unit weight (radial entry): $\frac{V _{w 2} u _{2}}{g}$
Outlet whirl: $V_{w 2} = u_{2} - \frac{V _{f 2}}{tan ϕ}$ ( $ϕ$ = outlet vane angle measured from the tangent)
Discharge: $Q = π D_{2} B_{2} V_{f 2}$ (outlet width $B_{2}$ )

Backward-curved vanes ( $ϕ < 90°$ ) are standard — they give a stable, non-overloading power characteristic.

Minimum starting speed

Flow begins only when the centrifugal head developed exceeds the manometric head:

\frac{u _{2}^{2} - u _{1}^{2}}{2 g} \geq H_{m} \Rightarrow N_{min} = \frac{120 η _{man} V _{w 2} D _{2}}{π ( D _{2}^{2} - D _{1}^{2} )}

(the second form uses $H_{m} = η_{man} V_{w 2} u_{2} / g$ ).

Multistage pumps

Impellers in series (on one shaft) — for high heads: total head $= n \times H_{m}$ , same discharge.
Pumps in parallel — for large discharge: total discharge $= n \times Q$ , same head.

Specific speed and similarity

FormulaPump specific speed and laws

Specific speed: $N_{s} = \frac{N Q}{H _{m}^{3/4}}$ — speed of a similar pump delivering 1 m³/s against 1 m head. Low $N_{s}$ → radial-flow (centrifugal, high head, small discharge); medium → mixed-flow; high → axial-flow (low head, large discharge).

Model laws (similar pumps): $\frac{Q}{N D ^{3}}$ , $\frac{g H}{N ^{2} D ^{2}}$ , $\frac{P}{ρ N ^{3} D ^{5}}$ constant.

Affinity laws (same pump, changed speed): $Q \propto N$ , $H \propto N^{2}$ , $P \propto N^{3}$ . (Same speed, trimmed impeller: $Q \propto D$ , $H \propto D^{2}$ , $P \propto D^{3}$ approximately.)

Characteristic curves and operating point

Main characteristics — $H_{m}$ , power and $Q$ plotted against speed.
Operating characteristics (constant design speed) — $H_{m}$ , shaft power and $η_{o}$ against $Q$ . Head is highest at zero flow (shut-off head) and falls as $Q$ rises; efficiency peaks at the design point (best efficiency point).
Constant efficiency (Muschel) curves.
System curve: $H = H_{s t a t i c} + K Q^{2}$ (friction and minor losses).
The operating point is the intersection of the pump $H$ – $Q$ curve and the system curve.

Cavitation and NPSH

When absolute pressure at the impeller eye falls to the vapour pressure, vapour bubbles form and collapse → noise, vibration, fall in head and efficiency, pitting of the impeller.

FormulaNet positive suction head

Available NPSH (pump above sump level):

N P S H_{A} = \frac{p _{a}}{ρ g} - \frac{p _{v}}{ρ g} - h_{s} - h_{f s}

Cavitation is avoided if $N P S H_{A} \geq N P S H_{R}$ (required, given by the manufacturer).

Thoma's cavitation factor for pumps: $σ = \frac{N P S H}{H _{m}}$

Theoretical maximum suction lift for water at sea level is about 10.3 m (atmospheric head), but practical suction lifts are much smaller because of vapour pressure, friction, velocity head and NPSH required.
Prevention: keep suction pipe short with large diameter and few bends, reduce suction lift (or use positive suction head/submergence), avoid running at excessive speed or far beyond the design flow.

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