Answer:
N = 38546.82 rpm
Explanation:
= 150 mm
![A_{1}= \frac{\pi }{4}\times 150^{2}](https://tex.z-dn.net/?f=A_%7B1%7D%3D%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Ctimes%20150%5E%7B2%7D)
= 17671.45 ![mm^{2}](https://tex.z-dn.net/?f=mm%5E%7B2%7D)
= 250 mm
![A_{2}= \frac{\pi }{4}\times 250^{2}](https://tex.z-dn.net/?f=A_%7B2%7D%3D%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Ctimes%20250%5E%7B2%7D)
= 49087.78 ![mm^{2}](https://tex.z-dn.net/?f=mm%5E%7B2%7D)
The centrifugal force acting on the flywheel is fiven by
F = M (
-
) x
------------(1)
Here F = ( -UTS x
+ UCS x
)
Since density, ![\rho = \frac{M}{V}](https://tex.z-dn.net/?f=%5Crho%20%3D%20%5Cfrac%7BM%7D%7BV%7D)
![\rho = \frac{M}{A\times t}](https://tex.z-dn.net/?f=%5Crho%20%3D%20%5Cfrac%7BM%7D%7BA%5Ctimes%20t%7D)
![M = \rho \times A\times t](https://tex.z-dn.net/?f=M%20%3D%20%5Crho%20%5Ctimes%20A%5Ctimes%20t)
![M = 7100 \times \frac{\pi }{4}\left ( D_{2}^{2}-D_{1}^{2} \right )\times t](https://tex.z-dn.net/?f=M%20%3D%207100%20%5Ctimes%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Cleft%20%28%20D_%7B2%7D%5E%7B2%7D-D_%7B1%7D%5E%7B2%7D%20%5Cright%20%29%5Ctimes%20t)
![M = 7100 \times \frac{\pi }{4}\left ( 250^{2}-150^{2} \right )\times 37](https://tex.z-dn.net/?f=M%20%3D%207100%20%5Ctimes%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Cleft%20%28%20250%5E%7B2%7D-150%5E%7B2%7D%20%5Cright%20%29%5Ctimes%2037)
![M = 8252963901](https://tex.z-dn.net/?f=M%20%3D%208252963901)
∴
-
= 50 mm
∴ F = ![763\times \frac{\pi }{4}\times 250^{2}-217\times \frac{\pi }{4}\times 150^{2}](https://tex.z-dn.net/?f=763%5Ctimes%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Ctimes%20250%5E%7B2%7D-217%5Ctimes%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Ctimes%20150%5E%7B2%7D)
F = 33618968.38 N --------(2)
Now comparing (1) and (2)
![33618968.38 = 8252963901\times 50\times \omega ^{2}](https://tex.z-dn.net/?f=33618968.38%20%3D%208252963901%5Ctimes%2050%5Ctimes%20%5Comega%20%5E%7B2%7D)
∴ ω = 4036.61
We know
![\omega = \frac{2\pi N}{60}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B2%5Cpi%20N%7D%7B60%7D)
![4036.61 = \frac{2\pi N}{60}](https://tex.z-dn.net/?f=4036.61%20%3D%20%5Cfrac%7B2%5Cpi%20N%7D%7B60%7D)
∴ N = 38546.82 rpm
Answer:
(a) the cutting time to complete the facing operation = 11.667mins
b) the cutting speeds and metal removal rates at the beginning= 12.89in³/min and end of the cut. = 8.143in³/min
Explanation:
check attached files below for answer.
Answer:
radius = 0.045 m
Explanation:
Given data:
density of oil = 780 kg/m^3
velocity = 20 m/s
height = 25 m
Total energy is = 57.5 kW
we have now
E = kinetic energy+ potential energy + flow work
![E = \dot m ( \frac{v^2}{2] + zg + p\nu)](https://tex.z-dn.net/?f=E%20%3D%20%5Cdot%20m%20%28%20%5Cfrac%7Bv%5E2%7D%7B2%5D%20%2B%20%20zg%20%2B%20p%5Cnu%29)
![E = \dot m( \frac{v^2}{2] + zg + p_{atm} \frac{1}{\rho})](https://tex.z-dn.net/?f=E%20%3D%20%5Cdot%20m%28%20%5Cfrac%7Bv%5E2%7D%7B2%5D%20%2B%20%20zg%20%2B%20p_%7Batm%7D%20%5Cfrac%7B1%7D%7B%5Crho%7D%29)
![57.5 \times 10^3 = \dot m ( \frac{20^2}{2} + 25 \times 9.81 + 101325 \frac{1}{780})](https://tex.z-dn.net/?f=57.5%20%5Ctimes%2010%5E3%20%3D%20%5Cdot%20m%20%28%20%5Cfrac%7B20%5E2%7D%7B2%7D%20%2B%2025%20%5Ctimes%209.81%20%2B%20101325%20%5Cfrac%7B1%7D%7B780%7D%29)
solving for flow rate
![\dot m = 99.977we know that [tex]\dot m = \rho AV](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%2099.977%3C%2Fp%3E%3Cp%3Ewe%20know%20that%20%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cdot%20m%20%20%3D%20%5Crho%20AV)
![\dot m = 780 \frac{\pi}{4} D^2\times 16](https://tex.z-dn.net/?f=%5Cdot%20m%20%20%3D%20780%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20D%5E2%5Ctimes%2016)
solving for d
![99.97 = 780 \times \frac{\pi}{4} D^2\times 16](https://tex.z-dn.net/?f=99.97%20%3D%20780%20%5Ctimes%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20D%5E2%5Ctimes%2016)
d = 0.090 m
so radius = 0.045 m
C my friend 20 characters suck