Answer to Question #126597 in Mechanical Engineering for Dorado

Question

c) A 50 mm-diameter propeller was installed in a 150 mm-diameter water pipe and the propeller speed was measured for a range of water discharge in the pipe. The water had a density and dynamic viscosity of 1000 kg/m3 and 0.00112 Ns/m2 respectively. The measured results were as follows:

Q (litres/s): 12 28 45 63 95 120 160 180
N (rps): 5 10 15 20 30 40 60 80
Plot the dependence of propeller coefficient against propeller Reynolds number. A geometrically similar propeller with diameter 100 mm was installed in a 300 mm-diameter pipe conveying oil with density 800 kg/m3 and dynamic viscosity 0.007 Ns/m2 . Estimate the discharge in the oil pipe for measured propeller speeds of 40 rps and 90 rps.

Answer 1

propeller diameter=50 mm, diameter of pipe=150 mm, density of water=1000 kg/m3, and dynamic viscosity=0.00112 $\frac{Ns}{m^2}$ ,

Q (litres/s): 12 28 45 63 95 120 160 180

N (rps): 5 10 15 20 30 40 60 80

Now, for taking different flow rate we will find different velocity and then its related Reynold's number

$Q_x=\frac{\pi}{4}d^2V_x$

$V_x=0.0637 Q_X$

we will put different value of Q and then we get V

V (m/s) : .76 1.78 2.86 4.01 6.05 7.64 10.2 11.46

$Re=\frac{\rho\times v\times d}{\mu}$

Re= 89285$\times v$

Re (1) : 67857.14 158928.57 255357.14 358035.71 540178.57 910714.28 1023214.2

now similarly we will get data for other

Re(2) : 54321.22 178322.33 268934.22 389465.22 609234 1023657 1126493.3