The experiment was done with two different plates a yellow at the beginning for 1200 and 1400 rpm, and then with a black plate 1200 and 1400 rpm as well./n Introduction A centrifugal pump consists of a rotating impeller enclosed in a housing. The impeller is a set of blades attached to a disk. As the impeller rotates, the blades add kinetic energy to the fluid as it flows in a radial direction (i.e. perpendicular to the rotating shaft). The housing shape is designed so that the high-velocity fluid leaving the outer edge of the impeller is decelerated as it approaches the pump exit, leading to an increase in fluid pressure. The PumpLab™ apparatus is designed so that the impeller and its blades are easily viewable. The geometry of the blades, especially their angle with respect to the direction of disk rotation, has a significant impact on the characteristics of the pump. In an application requiring a centrifugal pump, an engineer must first determine the range of flow rates required as well as the pressure (or head) that the pump must deliver to overcome the frictional losses in the piping system of interest. The pump must be chosen so that its head versus flow rate characteristic matches the demand imposed by the piping system. Manufacturer's catalogs will usually present the head and flow rate data in graphical or tabular form at a particular operating speed. The main goal of this experiment is to measure the operating characteristics of a typical centrifugal pump at two operating speeds and compare the results with theoretical expectations. Background The energy equation for incompressible flow (e.g. Equation 5.84 and 5.85 in Fundamentals of Fluid Mechanics by Munson et al, 5th edition) applied to a control volume around the pump can be written as: Pout γ + V2 out 2g Pin + Zout in V. 2g + +Zin (hshL)P (1) and W shaft = YQhs (2) In these equations, h¸ represents shaft head and h is the head loss in the pump. For a typical pump, both velocities are equal (from continuity, assuming inlet and outlet flow areas are the same) and the difference in height is negligible. It is often convenient to express the measured pump head (hp) as: hp = (hs-hL)p (3) If one assumes that h₂ is zero in Equation 3 (i.e. there are no losses in the pump), then the shaft power calculated from Equation 2 will be an ideal value. Thus: hp = Pout-Pin Y and Wideal = yQhp Combining Equations 4 and 5 gives: Wideal - = Q(Pout Pin) (4) (5) (6) Generally, measured pump parameters such as power, head, and efficiency are plotted or tabulated versus flow rate for a particular speed. Since particular applications of the pump may dictate a different operating speed, it is often desirable to plot a pump's operating characteristic in terms of dimensionless parameters so that they are more generally useful. For example, dimensionless characteristics from a small laboratory pump can be used to predict the performance of a larger pump of the same design, or predict the effect of speed variations on parameters such as head and flow rate. In our case, measurements taken at two different speeds will be plotted on a single dimensionless curve, which could then be used to predict the pump performance at any other speed. Key dimensionless parameters are defined as: Q Co = (Flow Coefficient) @D³ ghp CH= (Head w² D² W shaft (Power Coefficient) CP pw³ D5 Coefficient) (7) (8) (9) where D = impeller diameter and @ = rotational speed in radians/sec. Pump efficiency may be defined a couple of different ways, based on whether it is a combined pump-motor efficiency or just for the pump only. In our case, the input torque is measured so the efficiency is just for the pump: n Wideal W shaft YQhp Τω (10) where Tshaft torque. Ideal centrifugal pump characteristics can be predicted knowing impeller geometry and pump speed. Section 12.4 in Munson may be reviewed for the analysis details. Figure 1, taken from Munson, shows the important elements of the geometry of a typical impeller. (a) W2 W2 V2 B21 αz Vr2 Ve2- U2 (c) V2 B27 az ai U2 W₁ βι Ve1 Vri U1 (b) Figure 1: Velocity diagrams for Impeller (Munson, 5th Ed.) The velocity vectors in this diagram are defined as follows: W is the fluid velocity relative to the impeller, U is the velocity of the blade, and V is the absolute velocity = W + U. Note that these quantities, along with the angles ẞ and a, are defined at the impeller inlet (subscript 1) and impeller exit (subscript 2). An ideal head (h;) - flow rate (Q) characteristic can be derived (see Eqn 12.18 in Munson, 5 th Ed.) which is: w² r₁₂ h₁ = g wr2 cot B2 Q 2r2b28 (11)

Fig: 1