A 50 mm diameter thin walled pipe is covered with an insulation layer with thicknessof 25mm and thermal conductivity of0.075W/mK. The inner pipe carries a superheated vapor at atmospheric pressure. The steam temperature entering the pipe is 120°Candthe air temperature is 20°C. The convection heat transfer coefficient on top of the insulation layer is 15W/m(K. If the velocity of the steam is 10 m/s, at what point along the pipe the steam starts to condense?

The steam will start to condense at 6.6 mm into the pipe

Explanation:

The volume flow rate =π×(50/1000)²/4×10 = 0.0196 m³/s

The specific volume of the steam = 1.769 m³/kg

Therefore;

The mass flow rate = 0.0196/1.769 = 0.011099  kg/s

The resistance of the insulation material = ln(0.075/0.05)/(2×π×0.075) = 0.860 K/W

The resistance of the outside film of the insulator = 1/(15×2×π×0.075×1) = 0.14147 K/W

The total resistance = 0.14147 + 0.860 = 1.00147 K/W

1/(UA) = 1.00147 K/W

A = 2×π×0.05×1

1/U = 0.3146

U = 3.178 W/m² K

We have;

T(x) = T₀ + (Tin - T₀) exp(-UπDx/mcp)

Therefore, when T(x) = 100°C, we have;

100 = 20 + (120 - 20)exp(-3.178×π×0.05x/(0.011099 × 1.33))

Solving, we get

x = 6.597× 10⁻³ m ≈ 6.6 mm

Therefore, the steam will start to condense at 10 mm into the pipe.

the body's situation won't change the forces are equal opposit and on the same body

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )