A stirred tank is considered, operating at atmospheric pressure, fed with two fluxes having variable volumetric flows F 1 (t) and F 2 (t), temperatures T o 1 and T ∘ 2 , specific heats c p1 = c p2 = c...

A stirred tank is considered, operating at atmospheric pressure, fed with two fluxes having variable volumetric flows F₁(t) and F₂(t), temperatures T^o
₁
and T^∘
₂, specific heats c_p1
= c_p2
= c_p
and densities ρ₁
= ρ₂
= ρ (Fig. 3.19).

Both fluxes contain a dissolved material having the molar concentrations C₁, and C₂
respectively. The output flow is F(t), with concentration C(t), density ρ, and specific heatc_p. It is supposed the tank is perfectly stirred and the mixing is done without additional heat and without heat exchange with the exterior.

The values of densities, specific heat, of the inputs and outputs are considered equal. Considering the dependence of the output flow F(t) function of the tank liquid content (variable)
 one has to determine the following:

(a) The dynamic mathematical model of the stirred tank taking care to evidence the unknowns: C(t), T^∘(t)andV(t). There will be considered:

– input variables: the volumetric flows F₁(t)siF₂(t).

 – output variables: output flow concentration C(t), output flow temperature T^∘(t), and tank liquid volume V(t).

(b) Which way does the dynamic mathematical model change when the heat losses are not negligible? (the heat transfer coefficient is K_T
and heat transfer area of the tank is A_T), the evacuation of the tank is done at the height H (dotted line in the figure). The characteristics of the hydraulic circuit (ξ , λ , l_p, d_p
etc.) are assumed to be known.