Respuesta :
Answer:
T = 52.76 ft . lbf
Explanation:
Given data:
inner diameter of cylinder 4 in
height of cylinder 8 in
gap width = 0.001 in
we know shear force is given as
[tex]F =\tau A = \tau (2\pi RH) [/tex]
Where, [tex]\tau[/tex] is torque acting on cylinder
[tex]\tau = \mu \frac{V}{d} = \mu \frac{ R\omega}{d}[/tex]
[tex]\mu[/tex] is kinematic viscosity, for castor oil at 90 degree F = 0.259 N s/m^2
substituing all value in shear force formula we get
[tex]F = \frac{2\pi \mu R^2\omega h}{d}[/tex]
we know that
[tex]Torque, T = force \times R[/tex]
[tex]T = \frac{2\pi \mu R^3\omega h}{d}[/tex]
[tex]T = \frac{2\pi (0.259\times 2.09\times 10^{-2}\times 2^3\times 400\times 8 }{10^{-3}} \times 2\pi \times \frac{1 min}{60} \times \frac{1 ft^3 }{1728 in^3}[/tex]
T = 52.76 ft . lbf
The torque required to turn the inner cylinder at 400 rpm is; 77.4 lb.ft
What is the Torque?
We are given;
Diameter; d = 4 in
radius; R = 2 in = 2/12 ft
Clearance Gap = 0.001 in
angular speed; ω = 400 rpm = 41.8879 rad/s
height; h = 8 in
The formula to find the torque from different derivations is;
T = 2πμR³ωh/d
where;
μ is viscosity
R is radius
ω is angular speed
h is height
d is clearance gap
At 90°F castor oil, μ = 0.007942 lbf.s/ft²
Thus;
T = (2π * 0.007942 * (2/12)³ * 41.8879 * 8)/0.001
T = 77.4 lb.ft
Read more about Torque at; https://brainly.com/question/20691242
