Example 1: Application of Angular Momentum to a Reaction Turbine¶
Application of angular momentum often involves use of continunity and energy (bernoulli’s equation). Selection of CV is important to make analysis straightforward. Consider the following example involving a reaction turbine (like a Rain-Bird)
The problem statement is depicted in Fig. 123
Fig. 123 Caption¶
Apply continunity as in Fig. 124
Fig. 124 Caption¶
Then momentum as in Fig. 125
Fig. 125 Caption¶
Continue the analysis (break the CV into upper and lower arm, use symmetry to cancel the volume integrals) as in Fig. 126
Fig. 126 Caption¶
Complete the analysis as in Fig. 127
Fig. 127 Caption¶
now apply ENGR-1330 to perform the calculations.
# computational thinning
import math
q = 0.1 #discharge
v_jet = 50.0
omega = 500*2*math.pi/60
radius = 0.5
rho = 1000.0
power = rho*q*v_jet*radius*omega - rho*q*omega**2*radius**2
print("Power ",round(power,2)," Newton-meters/sec ")
Power 62360.77 Newton-meters/sec
Example 2: Application of Angular Momentum to a Reaction Turbine¶
Here we will do the same problem, but using a fixed reference frame CV
Fig. 128 Caption¶
Fig. 127 is analysis of the volume integral in a vector representation of the moment of momentum
Fig. 129 Caption¶
Fig. 127 is analysis of the flux integrals in a vector representation of the moment of momentum After the equations are constructed, the analysys proceedes the same as in the earlier example.