Question
In a thermally insulated tube of cross section area 4cm2 there is a liquid of thermal expansion coefficient of 10–3 K–1 flowing. Its velocity at the entrance is 0.1 m/s. At the middle of the tube a heater of a power of 10 kW is heating the liquid. The specific heat capacity of the liquid is 1.5 kJ/(kg K), and its density is 1500 kg/m3 at the entrance.
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Find rise in temperature of the liquid as it pass through the tube :
ρ1v1A1 = ρ2v2A2
m = 1500 kg/m3 × 0.1 m/s × 4(cm)2
msΔT = 1000
1500 × 0.1 × 4 × 10–4 × 1500 × ΔT = 10000
ΔT = =
How much bigger is the volume rate of flow at the end of the tube than at the entrance in cubic meters?
no solution
What is the density of liquid at the exit ?
ρ2 = = = 1350
ρ2v2A2 = ρ1v1A1
⟹ 1350 × v2 = 1500 × 0.1
v2 = 0.11 m/s