Prandtl derived eq 653 in 1935 and then adjusted the

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Unformatted text preview: lve if Red is known and f is wanted. There are many alternate approximations in the literature from which f can be computed explicitly from Red 1/4 4000 Red 105 H. Blasius (1911) 0.316 Red f (6.55) 2 1.8 log Red Ref. 9 6.9 Blasius, a student of Prandtl, presented his formula in the first correlation ever made of pipe friction versus Reynolds number. Although his formula has a limited range, it illustrates what was happening to Hagen’s 1839 pressure-drop data. For a horizontal pipe, from Eq. (6.55), 1/4 L V2 L V2 p f 0.316 hf d 2g d 2g g Vd or p 0.158 L 3/4 1/4 d 5/4 7/4 V (6.56) at low turbulent Reynolds numbers. This explains why Hagen’s data for pressure drop begin to increase as the 1.75 power of the velocity, in Fig. 6.4. Note that p varies only slightly with viscosity, which is characteristic of turbulent flow. Introducing Q 1 2 4 d V into Eq. (6.56), we obtain the alternate form p 0.241L 3/4 1/4 d 4.75 Q1.75 (6.57) | v v For a given flow rate Q, the turbulent pressure drop decreases with diameter even mo...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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