9 Professor Walter Tunnel needs to measure the fl ow velocity in a water tunnel. Due to

Chapter 6, Problem p6.139

(choose chapter or problem)

9 Professor Walter Tunnel needs to measure the fl ow velocity in a water tunnel. Due to budgetary restrictions, he cannot afford a pitot-static probe, but instead inserts a total head probe and a static pressure probe, as shown in Fig. P6.139, a distance h1 apart from each other. Both probes are in the main free stream of the water tunnel, unaffected by the thin boundary layers on the sidewalls. The two probes are connected as shown to a U-tube manometer. The densities and vertical distances are shown in Fig. P6.139. (a) Write an expression for velocity V in terms of the parameters in the problem. (b) Is it critical that distance h1 be measured accurately? (c) How does the expression for velocity V differ from that which would be obtained if a pitot-static probe had been available and used with the same U-tube manometer? h1 h2 h3 U-tube manometer ptotal pstatic w m V P6.139