Surge tank objectives and economic penstock diameter factors

Objectives of a surge tank

A surge tank is an open shaft/chamber at the junction of the pressure tunnel and penstock. It is provided to:

1. Reduce water hammer pressure in the tunnel—the free surface reflects pressure waves so only the short penstock carries full water hammer.
2. Supply water quickly when turbine load increases (acts as a reservoir until tunnel flow accelerates).
3. Store water (rising level) when load is rejected, preventing excessive pressure rise.
4. Improve speed regulation of the turbine by reducing the effective length of the water column.

Factors governing the economical diameter of penstock

The economic diameter is the one giving minimum total annual cost (annual cost of the pipe + annual value of energy lost in friction). It depends on:

1. Discharge $Q$: larger flow needs larger diameter.
2. Head $H$ and pressure: higher heads need thicker plates, raising cost per unit diameter, so economic velocities are higher at high heads (smaller diameter relative to flow).
3. Length of penstock: head loss is proportional to length.
4. Cost of material and fabrication: steel price, plate thickness, welding, transport, anchor blocks and supports; higher cost favours smaller diameter.
5. Value (tariff) of energy: higher energy price favours a larger diameter to reduce losses.
6. Plant load factor and hours of operation: more running hours mean more energy lost through friction, favouring larger diameter.
7. Interest rate and life of penstock: affect the annual capital recovery cost.
8. Friction coefficient: pipe roughness (material, age, lining).
9. Water hammer and allowable velocity: larger velocity gives larger water hammer pressure and thicker pipe; erosion if silt-laden.
10. Transport and handling limits: maximum section size that can be carried on hill roads in Nepal.

Empirical formulas (e.g. USBR, Sarkaria, Fahlbusch) give a first estimate, refined by the cost-curve (graphical) method.