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ArbitrLikvidat [17]
3 years ago
11

Problem 6.2 7–14 Engine oil at 80°C flows over a 12-m-long flat plate whose temperature is 30°C with a velocity of 3 m/s. Determ

ine the total drag force and the rate of heat transfer over the entire plate per unit width.

Physics
1 answer:
Ber [7]3 years ago
4 0

Answer:

A) Drag force = 88.02 N

B) Rate of heat transfer = 38,214 W

Explanation:

A) The properties of engine oil at temperature of; (Ts + T(∞))/2 =

(30 + 80)/2 = 55°C are;

From the table i attached, we get the following ;

Density(ρ) = 0.867 g/cm³ = 867 kg/m³

Viscocity (μ) = 0.1264 mm²/s = 12.64 x 10^(-5) m²/s

Also from the table, by interpolation;

Pr = 1551

k = 0.1414 W/m°C

Kinematic Viscosity (v) = 7.045 x 10^(-5) m²/s

Now, Reynolds number(Re) = VLc/v

Where V is the flow velocity,

v is the kinematic velocity,

Lc is the characteristic length.

Thus, Re = (3 x 12)/(7.045 x 10^(-5)) =

5.11 x 10^(5)

This is less than the critical Re, thus we have a laminar flow.

So, the friction coefficient,

Cf = 1.328 Re^(-0.5)

Cf = 1.328(5.11 x 10^(5))^(-0.5) = 0.00188

Drag force(Fd) = (Cf)(A)(ρV²/2) = 0.00188 x (12 x 1)((867 x 3²)/2) = 88.02 N

B) The Nusselt number is determined from:

Nu = hL/k = 0.664 x Re^(0.5) x  Pr^(1/3)

Nu = 0.664 x [5.11 x 10^(5)]^(0.5) x 1551^(1/3) = 5494.34

Thus, hL/k = 5494.34

h = (5494.34 x 0.1413)/12 = 64.69 W/m².k

Thus, rate of heat transfer per unit length is given as;

Q' = hA(T(∞) - Ts) = 63.69 x (12x1) x (80 - 30) = 38,214 W

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suter [353]

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Thrust developed = 212.3373 kN

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Assuming the ship is stationary

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power supplied to the propeller ( Punit ) = 1900 KW

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first step : <em>calculate the area of the duct </em>

A = π/4 * D^2

   =  π/4 * ( 2.6)^2  = 5.3092 m^2

<em>next : calculate the velocity of propeller</em>

Punit = (A*v*β ) / 2  * V^2     ( assuming β = 999 kg/m^3 ) also given V1 = 0

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<em>Finally determine the thrust developed </em>

F = Punit / V2

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3 years ago
How much does the angle of refraction change from 380nm to 700nm when the incident angle is 80?
allochka39001 [22]

Answer:

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It is known that the gravitational force of attraction between two alpha particles is much weaker than the electrical repulsion.
natali 33 [55]

Answer:

<em>The ratio of gravitational force to electrical force is 3.19 x 10^-36 </em>

<em></em>

Explanation:

mass of an alpha particle = 6.64 x 10^{-27} kg

charge on an alpha particle = +2e = +2(1.6 x 10^{-19} C) = 3.2 x 10^{-19} C

distance between particles = d

For gravitational attraction:

The force of gravitational attraction F = \frac{Gm^{2} }{r^{2} }

where G = gravitational constant = 6.67 x 10^{-11} m^3 kg^-1 s^-2

r = the distance between the particles = d

m = the mass of each particle

therefore, gravitational force = \frac{6.67*10^{-11}*(6.64*10^{-27} )^{2}  }{d^{2} } = \frac{2.94*10^{-63} }{d^{2} }  Newton

For electrical repulsion:

Electrical force between the particles = \frac{-kQ^{2} }{r^{2} }

where k is the Coulomb's constant = 9.0 x 10^{9} N•m^2/C^2

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Q = charge on each particle

therefore, electrical force = \frac{-9*10^{9}*(3.2*10^{-19} )^{2}  }{d^{2} } = \frac{-9.216*10^{-28} }{d^{2} } Newton

the negative sign implies that there is a repulsion on the particles due to their like charges.

Ratio of the magnitude of gravitation to electrical force = \frac{2.94*10^{-63} }{9.216*10^{-28} }

==> <em>3.19 x 10^-36 </em>

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Such reactions are called endothermic reactions.

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