The following type of nozzle problem is found in some introductory-level physics textbooks.1–3 The (average) flow speed of water through and out a hose with a cross-sectional area AH is vH. If a nozzle with an exit area AN < AH is attached to the hose, what is the speed vN of the water out of it? The books simply apply the continuity equation AHvH = ANvN to the nozzle to obtain vN = (AH/AN)vH. This solution is not correct because it does not take account of the fact that attaching the nozzle to the hose reduces the flow speed in it. So the books' values of vN must always be too high, sometimes by large amounts. It should not seem surprising that it takes more time to fill a watering can with a garden hose when there is a nozzle at the end of it than when there isn't. This paper will explain how a water nozzle actually works, and for a situation with a simple water source, the correct flow speed from a nozzle will be derived.

Topics
Educational aids, Equations of fluid dynamics, Books
1.
J.D. Cutnell and K.W. Johnson, Physics, 6th ed. (Wiley, New York, 2004), pp. 314–315.
2.
J. Walker, Physics, 2nd ed. (Pearson Education, Upper Saddle River, NJ, 2004), pp. 481–482. See also problem #41 on p. 497.
3.
R.A. Serway and J.W. Jewett, Physics for Scientists and Engineers with Modern Physics, 6th ed. (Brooks/Cole, Belmont, CA, 2004), pp. 432–433.
4.
See Ref. 1, p. 321.
5.
Technically, this is only the speed in the narrowest part of the hole's flow. It is called the vena contracta, and its distance from the hole is approximately equal to the hole's radius. See B.S. Massey, Mechanics of Fluids, 3rd ed. (Van Nostrand Reinhold, New York, 1975), pp. 84–85.
6.
See Ref. 2, pp. 488–489.
7.
Paul Peter Urone, College Physics, 2nd ed. (Brooks/Cole, Pacific Grove, CA, 2001), p. 285.
8.
A qualitative explanation of water nozzles resembling this one is given in L.A. Bloomfield, How Things Work: The Physics of Everyday Life, 2nd ed. (Wiley, New York, 2001), pp. 150–151.
9.
B.R. Munson, D.F. Young, and T.H. Okiishi, Fundamentals of Fluid Mechanics, 5th ed. (Wiley, Hoboken, NJ, 2006), pp. 719–721.
10.
The diagram has curves of the so-called friction factor versus Reynolds number for pipes with different internal roughnesses and diameters. The use of the curves is discussed in most fluid mechanics textbooks, such as C.T. Crowe, D.E. Elger, and J.A. Roberson, Engineering Fluid Mechanics, 8th ed. (Wiley, Hoboken, NJ, 2005), pp. 381–386.
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© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
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