A centrifugal water pump operates at 1750 rpm ; the impeller has backward-curved vanes with β2=6

step 1 In this problem, first calculating impaler exit radius. So it is given by exit radius that is eq

A centrifugal water pump operates at 1750 rpm ; the impeller...

A centrifugal water pump operates at $1750 \mathrm{rpm} ;$ the impeller has backward-curved vanes with $\beta_{2}=60^{\circ}$ and $b_{2}=1.25 \mathrm{cm} .$ At a flow rate of $0.025 \mathrm{m}^{3} / \mathrm{s},$ the radial outlet velocity is $V_{n_{2}}=3.5 \mathrm{m} / \mathrm{s}$. Estimate the head this pump could deliver at $1150 \mathrm{rpm}.$

Key Concepts

Pump Affinity Laws

These laws describe the relationships between the pump’s speed, flow rate, and head for geometrically similar pumps operating under the same conditions. In particular, the affinity laws state that the flow rate scales linearly with the rotational speed while the head scales with the square of the rotational speed. This concept is fundamental for predicting pump performance changes when operating at speeds different from the design point.

Centrifugal Pump Head Generation

In a centrifugal pump, the head developed is primarily related to the kinetic energy imparted to the fluid by the rotating impeller. This head depends on factors such as the peripheral (or tangential) velocity of the impeller and the design of the impeller vanes, which convert rotational kinetic energy into pressure. Understanding this principle is essential for estimating how changes in operating conditions, like rotational speed, affect the delivered head.

Velocity Triangle Analysis

The analysis of the velocity triangles at the impeller outlet helps in understanding how the fluid velocity components (radial and tangential) contribute to the pump’s performance. By decomposing the absolute velocity of the fluid into its components relative to the impeller’s motion, one can better interpret the pump’s design and predict how variations in geometry or operating speed will modify the energy transfer to the fluid.

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