Pumps

CE 356 HYDRAULIC ENGINEERING LAB

PUMP CHARACTERISTICS I. OBJECTIVES The objectives of this laboratory project are to 1. Perform experiments to determine the characteristic curves for a centrifugal pump operating at two different speeds (n1 and n2). 2. Use affinity (or similarity) laws to convert the characteristic curve measured for speed n1 to speed n2. 3. Compare the characteristic curve calculated in Part 2 to measured values for speed n2. II. THEORETICAL BACKGROUND A. Pump Description 1) Classification There are two basic types of pumps: (a) positive-displacement pumps (PDPs) and (b) dynamic or momentum-change pumps. Positive-displacement pumps have a moving boundary that forces the fluid to flow by changes in the volume of one or more chambers within the pump. An example of a PDP is a mammal's heart. Some advantages of PDPs are that they are capable of delivering almost any fluid regardless of viscosity, and the flow rate has only a weak dependence on the head against which the pump is working (because of the "positive displacement" associated with the volume changes within the pump). On the other hand, dynamic pumps add momentum to the fluid as it passes through an impeller. Dynamic pumps generally provide a higher flow rate than PDPs and a steadier discharge (as compared to the PDPs that frequently deliver the flow in pulses), but dynamic pumps are ineffective in handling high viscosity fluids. Dynamic pumps are classified as rotary or special design pumps. Rotary (or rotodynamic) pumps are the most common and can be divided into two groups with one of those groups being further divided into two types of pumps: •

•

centrifugal - radial flow (The flow leaves the impeller in the radial direction.) - mixed flow (The flow leaves the impeller in a direction between the radial and axial directions.) axial flow (The flow goes through the impeller in the axial direction like a fan.)

This laboratory project examines the performance of a radial-flow centrifugal pump. 2) Centrifugal Pump A cutaway schematic of a centrifugal or radial flow pump is shown in Fig. 1. A motor or engine drives the impeller by supplying a torque through a shaft. The impeller converts this mechanical energy into hydraulic energy in the fluid. The fluid enters the pump axially through the suction port of the pump housing and then through the eye of the impeller. The rotating impeller whirls the fluid tangentially, then centrifugal action causes the fluid to move radially

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outward. The work done by the impeller on the fluid increases the head of the fluid as it passes through the impeller. This increase in head comes from both the increased velocity as the fluid passes through the impeller and the increased pressure. When the liquid exits the impeller and enters the spiral casing (called the volute), most of the velocity head is converted into pressure head. The fluid then leaves the volute through a tangential discharge port.

Fig. 1 - Centrifugal Pump B. Characteristic Curves Pump characteristic curves (Fig. 2) show the performance characteristics of the pump, i.e., the relations of the pump head (hp), the efficiency (η), and the brake horsepower (not shown here) to the flow rate (Q). A system curve (or system characteristic curve) shows the head required for various flow rates in the piping system. For most situations, the head requirement consists of the head required for the static lift, or the change in elevation (∆z) from the upstream end of the piping system to the downstream end, and for the head losses, which are a function of the velocity head (V2/2g or Q2/{2gA2}). The operating point is the point at which the available pump head (hp) equals the head (Hs) required by the system, where Hs = ∆z + (K V2/2g) and K is a general representation for the loss coefficients, including f L/D for frictional losses. C. Similarity or Affinity Laws If two pumps are geometrically and dynamically similar, their flow rates, pump heads, and water powers for homologous operation are related by

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Rating is at point of maximum efficiency. Qr = Rated discharge. (hp)r = Rated head. The head for Q = 0 is called the shutoff head.

Fig. 2 - Pump Characteristic Curves Q2 n 2  D2    = Q1 n1  D1  (h p )2

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P2 ρ 2  n 2    = P1 ρ1  n1 

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n  =  2  ( h p )1  n1 

3

(1)

 D2  D  1

   

 D2  D  1

   

2

(2)

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(3)

where n = rotational speed, D = impeller diameter (or any representative size), P = water power (γQHp), γ = specific weight = gρ, g = acceleration of gravity, and ρ = density. For the same pump with the same fluid (so that D and γ do not change),

Q2 n 2 = Q1 n1 (h p )2 ( h p )1

=

(4)

 n2  n  1

P2  n 2  =  P1  n1 

   

2

(5)

3

(6)

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Eqs. 3 and 6 assume that the efficiency of the pump does not change as the speed of rotation and/or the pump sizes change. III. LABORATORY APPARATUS A. Head

The experimental pump in the laboratory has a differential mercury manometer between the suction side (1) and the discharge side (2), as shown in Fig. 3, to evaluate the head (hp) produced by the pump. There is also a pressure gage connected to the discharge side of the pump, but the pressure gage will not be used for these experiments. The energy equation between points 1 and 2 can be written as p1 V12 p 2 V22 z1 + + + h p − h L − Σh ' = z 2 + + 2g 2g γ γ

(7)

where hL = frictional head loss between 1 and 2 and Σh′ is the sum of all of the minor losses. Assuming that the piezometer taps are placed so that hL and Σh′ are negligibly small, Eq. 7 becomes  V2    2g   

h p = ∆h + ∆

(8)

Fig. 3 - Schematic Diagram of Laboratory Pump

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where ∆ is defined as the value at 2 minus the value at 1 and h = piezometric head, which is defined as

h=z+

p γ

(9)

For the mercury manometer, using the symbols in Fig. 3, p1 − γλ1 + γ m R − γR + γλ 2 = p 2

(10)

Dividing by γ, using (λ1 - λ2) = (y2 - y1), and rearranging terms, the result can be written as γ  h 2 − h1 = ∆h =  m − 1 R  γ 

(11)

where γm = specific weight of manometer fluid (mercury in this experiment) and γ = specific weight of the fluid in the pipe (water). Thus, using the manometer, ∆h can be obtained from Eq. 11. (Note that, since Eq. 10 is general and applicable to any manometer, Eq. 11 demonstrates that a differential manometer actually measures the difference in piezometric head between two points. If the elevation difference between the two points is also known, then the differential manometer can be used to determine the pressure difference.) Combining Eqs. 8 and 11 gives  V2   γ + m  2g   γ   

h p = ∆



− 1 R

(12)



The change in velocity head in Eq. 12 can be calculated from the measured flow rate and continuity. For this apparatus, D1 = D2 = 1 in. If pressure gages were used, ∆h in Eq. 8 would come from the measured pressures and elevations and the definition in Eq. 9. B. Flow Rate

In this experiment, the flow rate from the pump is measured volumetrically from the time required for a measured volume of water to flow into a tank. C. Power

The water power is the power transferred from the impeller to the water. It can be calculated from the flow rate and the pump head, and is called Pout since it is the power delivered by the pump: Pout = γh p Q

(13)

The power to the pump is the power supplied to the impeller through the shaft from the motor. This power is also called the shaft or brake power (or horsepower, if traditional English units are being used). In this experiment, the electrical input power to the motor is measured by measuring the voltage (E) across the motor and the current (I) through the motor. The input power to the motor is then Pin = EI

(14)

With E in volts and I in amperes, P is then in watts (joule/s or m N/s).

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D. Efficiency

The overall efficiency of a pump and motor together (ηo) is the ratio of the output power to the input power: P ηo = out Pin

(15)

Although some large pumps can operate at efficiencies as high as about 92%, most have efficiencies of 50% to 80%. The pump in the lab is very small so its efficiency is very low. The value of ηo for this experiment is lower than the ratio of the water power to the brake power since ηo also includes losses in the motor for converting electrical energy to mechanical energy. IV. REPORT

The TA will give you the pump speeds to be used in the experiments. Let the lower speed be n1 and the higher speed be n2. 1) Introduction: A brief description of the experiment and the report. 2) Computations and Results: Show sample calculations with labels, units, conversion factors, and explanations. Include Tabulation of lab measurements. Tabulations of calculations. hp, Q, Pin, Pout & ηo for n1. hp, Q, Pin, Pout & ηo for n2. Sample calculations. The rated hp and Q and the specific speed for each speed. Scale the measured hp, Q, Pin, and Pout for n2 to n1 using the similarity relationships and compare the scaled values with those measured for n1. For the rated conditions for n2, calculate the head loss between manometer tap 1 and the suction port of the pump. Comment on whether this loss is negligible, as assumed in obtaining Eq. 8. 3) Graphs: Characteristic curves. hp, Pin, & ηo vs. Q for n1. hp, Pin, & ηo vs. Q for n2. Comparison of measured hp, Q, Pin, and Pout for n1 with values calculated (scaled) from the measured values for n2. V. REFERENCES

1. McCabe & Smith, Unit Operations of Chemical Engineering, New York: McGraw-Hill Book Company, Inc., 1976 pp. 186-194. 2. White, Frank M., Fluid Mechanics, New York: McGraw-Hill Book Company, Inc., 1976 pp. 633-638, 642-651.

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