Step 1: Understanding the Concept:
Centrifugal pump turbomachinery fluid dynamics: the spiral volute casing features a gradually expanding cross-sectional area around the impeller periphery, decelerating high-velocity liquid discharge to convert kinetic velocity head ($
rac{v^2}{2g}$) into static pressure head ($
rac{P}{
ho g}$) via Bernoulli's principle.
Key Formula or Approach:
\[ \text{Volute Expansion: Area } (A) \uparrow \implies \text{Velocity } (v) \downarrow \implies \mathbf{\text{Kinetic Energy } \left(\frac{v^2}{2g}\right) \xrightarrow{\text{Converted to}} \mathbf{Pressure \text{ } Energy } \left(\frac{P}{\rho g}\right)} \]
Step 2: Detailed Explanation:
In centrifugal pump design and fluid hydraulics:
- High-speed rotation of the pump impeller imparts massive kinetic energy to the fluid, discharging it outward at high velocity:
1. Volute Casing (C): A curved, spiral casing surrounding the impeller with a cross-sectional area that increases progressively from the cut-water tongue to the discharge outlet.
2. According to the continuity equation ($Q = A \cdot v$), as the flow area ($A$) gradually widens, fluid velocity ($v$) is smoothly decelerated without generating turbulent eddies.
3. By Bernoulli's theorem, this controlled deceleration converts dynamic kinetic energy (velocity head) into useful static pressure energy (pressure head), minimizing hydraulic friction losses before the liquid enters the discharge pipe.
Step 3: Final Answer:
Therefore, the function of volute casing is to Convert kinetic energy in to pressure energy, corresponding to option (C).