In testing a model of reduced size under the previous conditions, complete hydraulic similarity will not be secured unless the relative roughness of the impeller and pump casing surfaces are the same. With the same surface texture in model and prototype, the model efficiency will be lower than that of the prototype, and greater relative clearances and shaft friction in the model will also reduce its efficiency.

The efficiency of a pump model can conveniently be stepped up to match the prototype efficiency by applying a formula of the same general form as the Moody formula used for hydraulic turbines:

The exponent n should be determined for a given laboratory and given type of pump on the basis of an adequate number of comparisons of the efficiencies of models and prototypes, with consistent surface finish in model and prototype. The Hydraulic Institule Stan n dards2 states that n has been found to vary from zero (when the surface roughness and clearances of the model and prototype are proportional to their size) to 0.26 (when the absolute roughness is the same in both).

When model tests are to serve as acceptance tests, it is generally recommended that the efficiency guarantees be stated in terms of model performance rather than in terms of calculated prototype performance. In the absence of such a provision, the efficiency stepup formula and the numerical value of its exponent should be clearly specified or agreed upon in advance of tests.

The Hydraulic Institute ANSI/HI 2000 Edition Pump Standards (Reference 10) give an example of model testing as follows:

example A single-stage pump to deliver 200 ft3/s (5.66 m3/s) against a head of 400 ft (122 m) at 450 rpm and with a positive suction head, including velocity head, of 10 ft (3 m) has an impeller diameter of 6.8 ft (2.lm). The pump being too large for a shop or laboratory test, a model with an 18-in (0.46-m) impeller is to be tested at a reduced head at 320 ft (97.5 m). At what speed, capacity, and suction head should the test be run? Applying the above relations:

in USCS units N1 — N D — 450 (|4) a/tI0 — 1825 rpm 1 D V H V 1.5/ A 400 r q1—q (D )2 S—200 (S)2 A§—8.73 ft3/s—3920 gpm

/ 2 1 \2 /97 5 in SI units N1 — 450( O46 ) A^^ — 1825 rpm

To check these results, the specific speed of the prototype is in USCS units Ns — N ^ — 450 — 71.2 in the ft3/s system s H3/4 4003/4

in SI units Ns — 45015-66. — 39 in the m3/s system s 1223/4

and that of the model is

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