Small spherical particles of diameter D = 50 μ m contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of ρ = 999 k g / m 3 , k = 1.2 W / m ⋅ K , and c p = 1200 J / k g ⋅ K , respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
Small spherical particles of diameter D = 50 μ m contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of ρ = 999 k g / m 3 , k = 1.2 W / m ⋅ K , and c p = 1200 J / k g ⋅ K , respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
Solution Summary: The author calculates the heat transfer rates at two surfaces for a wall section of an area A by using the equation Fourier’s law at X=-L.
Small spherical particles of diameter
D
=
50
μ
m
contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of
ρ
=
999
k
g
/
m
3
,
k
=
1.2
W
/
m
⋅
K
,
and
c
p
=
1200
J
/
k
g
⋅
K
, respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
3
N2=28
P(diametral pitch)=8 for all gears
Coupled to 25 hp motor
N3=34
Full depth spur gears with pressure angle=20°
N₂=2000 rpm
(1) Compute the circular pitch, the center-to-center distance, and base circle radii.
(2) Draw the free body diagram of gear 3 and show all the forces and the torque.
(3) In mounting gears, the center-to-center distance was reduced by 0.1 inch.
Calculate the new values of center-to-center distance, pressure angle, base circle radii,
and pitch circle diameters.
(4)What is the new tangential and radial forces for gear 3?
(5) Under the new center to center distance, is the contact ratio (mc) increasing or
decreasing?
2. A flat belt drive consists of two 4-ft diameter cast-iron pulleys spaced 16 ft apart.
A power of 60 hp is transmitted by a pulley whose speed is 380 rev/min. Use a
service factor (Ks) pf 1.1 and a design factor 1.0. The width of the polyamide A-3
belt is 6 in. Use CD=1. Answer the following questions.
(1) What is the total length of the belt according to the given geometry?
(2) Find the centrifugal force (Fc) applied to the belt.
(3) What is the transmitted torque through the pulley system given 60hp?
(4) Using the allowable tension, find the force (F₁) on the tight side. What is the
tension at the loose side (F2) and the initial tension (F.)?
(5) Using the forces, estimate the developed friction coefficient (f)
(6) Based on the forces and the given rotational speed, rate the pulley set. In other
words, what is the horse power that can be transmitted by the pulley system?
(7) To reduce the applied tension on the tight side, the friction coefficient is
increased to 0.75. Find out the…
The tooth numbers for the gear train illustrated are N₂ = 24, N3 = 18, №4 = 30, №6 = 36, and
N₁ = 54. Gear 7 is fixed. If shaft b is turned through 5 revolutions, how many turns will shaft a make?
a
5
[6]
b
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