Applications Consider problems with the simplifications a 1

Applications Consider problems with the simplifications : a) 1 -D flow b) Steady or steady-in-the mean cyclical flow c) The component of RTT resolved along the axis of rotation is existing.

Rotating Water Sprinkler The linear momentum flow from the outlets of the sprinkler arm ends will exert a force on the arm ends and cause a torque to rotate the arm along the sprinkler axis.

Applying the moment of momentum equation Eq. (6. 29) to the fixed control volume shown in Fig. (6. 12) we write We note that the angular momentum at the inlet, section (1) is zero because and the axis of rotation are perpendicular and the angular momentum a the outlet control surface, section (2) is :

here is the absolute velocity measured relative to the fixed control surface and for the sprinkler where is the relative velocity of the nozzle exit flow measured relative to the nozzle, and is the velocity of the moving nozzle measured relative to fixed control surface.

Euler’s Turbine Equation The Euler’s Turbine Equation relates the torque and the net flow of the angular momentum of a rotating machine where the sign of is positive, if direction and vice versa. The shaft work per unit mass for and U are in the same

Example 5. 19 • An air fan has a bladed rotor of 12 -in. outside diameter and 10 -in. inside diameter as illustrated in Figure E 5. 19 a. The height of each rotor is constant at 1 in. from blade inlet to outlet. The flowrate is steady, on a time-average basis, at 230 ft 3/min, and the absolute velocity of the air at blade inlet, V 1, is radial. The blade discharge angle is 30° from the tangential direction. If the rotor rotates at a constant speed of 1725 rpm, estimate the power required to run the fan. 6

Example 5. 19 (Because Wr 2 = Vr 2= W 2 sin 30˚) >> Note that these are same direction, unlike the sprinkler example 7