A tank shown in Figure-2 below is used to mix methanol and salt. initially contains 1 m³ of methanol. Salt is provided into the t a volumetric flow rate of Fsalt = 0.2 m³ s1. A stream with perfect methanol and salt leaves the tank with a volumetric flow F = 0.1 m³ s1. As the flow is unsteady, the volume of mixture in V(t), is a function of time.

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Chapter2: Matter And Energy
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b) A tank shown in Figure-2 below is used to mix methanol and salt. The tank
initially contains 1 m³ of methanol. Salt is provided into the tank with
a volumetric flow rate of Fsalt= 0.2 m³ s¹. A stream with perfectly mixed
methanol and salt leaves the tank with a volumetric flow rate of
F = 0.1 m³ s1. As the flow is unsteady, the volume of mixture in the tank,
V(t), is a function of time.
Fsalt=0.2 m³/s
Psalt=2160 kg/m³
V(t)
F=0.1 m³/s
Figure-2: A mixing tank of methanol and salt.
d(V (t)Psalt)
dt
Salt+methanol
The mass balance of salt in the tank is given by,
d(V (t) (Psalt +Pmethanol))
dt
= Fsalt Psalt - FPsalt
where Psalt is the density of salt and equal to 2160 kgm ³. The total mass
in the tank is given by,
= Fsalt Psalt - FPsalt - FPmethanol
where Pmethanol is the density of methanol and equal to 800 kgm-³. When
the tank contains V = 0.5m³ of mixture, what is the mass of salt in the tank?
Use the explicit Euler finite difference method to discretise the balance
equations.
(Hint: First, discretise the total mass equation to find time when the volume
of mixture is equal to V = 0.5m³).
Transcribed Image Text:b) A tank shown in Figure-2 below is used to mix methanol and salt. The tank initially contains 1 m³ of methanol. Salt is provided into the tank with a volumetric flow rate of Fsalt= 0.2 m³ s¹. A stream with perfectly mixed methanol and salt leaves the tank with a volumetric flow rate of F = 0.1 m³ s1. As the flow is unsteady, the volume of mixture in the tank, V(t), is a function of time. Fsalt=0.2 m³/s Psalt=2160 kg/m³ V(t) F=0.1 m³/s Figure-2: A mixing tank of methanol and salt. d(V (t)Psalt) dt Salt+methanol The mass balance of salt in the tank is given by, d(V (t) (Psalt +Pmethanol)) dt = Fsalt Psalt - FPsalt where Psalt is the density of salt and equal to 2160 kgm ³. The total mass in the tank is given by, = Fsalt Psalt - FPsalt - FPmethanol where Pmethanol is the density of methanol and equal to 800 kgm-³. When the tank contains V = 0.5m³ of mixture, what is the mass of salt in the tank? Use the explicit Euler finite difference method to discretise the balance equations. (Hint: First, discretise the total mass equation to find time when the volume of mixture is equal to V = 0.5m³).
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