1. The Ijsselmeer (Ijssel-lake) is an in-land bay in Europe and was recovered from the sea...

 

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1. The Ijsselmeer (Ijssel-lake) is an in-land bay in Europe and was recovered from the sea by building a 32 km long dyke between the sea and the now sweet water lake. Initially, the water in the Ijsselmeer was salt, but over time this lake became a sweet water lake because of a continuous inflow of sweet water from the river Ijssel. For this question, we are going to assume that the lake behaves as an ideally stirred vessel. The lake has an area of 1133 km² and an average depth of 4.4 meter. Sweet water (salt concentration 50 mg/L) is fed from the river at a rate of 1000 m³ per hour, and the same amount of water leaves the lake through the sluices in the dyke. We will assume that the initial salt concentration in the lake is the average salt concentration of sea water, namely 35 g/L. a. Write a general mass balance for the total amount of water in the lake and show that the mass of liquid in the lake remains constant at the initial value. b. Write a balance on the salt in the lake, to find a differential equation that describes the change in salt concentration with time. Do not forget the boundary condition. Try to not substitute values at this point but work with meaningful symbolic expressions for volume, flow rate, concentration, and time - this will come in handy later! C. Solve the differential equation to find an expression for the concentration as a function of time. Again, try to avoid substituting values but use symbolic expressions for volume, flow rate, concentration, and time. d. Plot the concentration of salt as a function of time for the described case. Now substitute the numbers you were given. Hint: you can use Excel or another helpful plotting tool. e. Calculate how long it takes before the concentration in the lake has dropped below 100 mg/L. f. If the inlet to the lake is increased to 1500 m³ per hour, how does this change your g. result? Describe or plot the results for this situation in comparison to the base case of 1000 m³ flow. How long does it take to get below 100 mg/L in this situation? When we let go of our assumption of the lake behaving like an ideally stirred tank reactor, what do you expect to happen? Describe and give reasoning. 1. The Ijsselmeer (Ijssel-lake) is an in-land bay in Europe and was recovered from the sea by building a 32 km long dyke between the sea and the now sweet water lake. Initially, the water in the Ijsselmeer was salt, but over time this lake became a sweet water lake because of a continuous inflow of sweet water from the river Ijssel. For this question, we are going to assume that the lake behaves as an ideally stirred vessel. The lake has an area of 1133 km² and an average depth of 4.4 meter. Sweet water (salt concentration 50 mg/L) is fed from the river at a rate of 1000 m³ per hour, and the same amount of water leaves the lake through the sluices in the dyke. We will assume that the initial salt concentration in the lake is the average salt concentration of sea water, namely 35 g/L. a. Write a general mass balance for the total amount of water in the lake and show that the mass of liquid in the lake remains constant at the initial value. b. Write a balance on the salt in the lake, to find a differential equation that describes the change in salt concentration with time. Do not forget the boundary condition. Try to not substitute values at this point but work with meaningful symbolic expressions for volume, flow rate, concentration, and time - this will come in handy later! C. Solve the differential equation to find an expression for the concentration as a function of time. Again, try to avoid substituting values but use symbolic expressions for volume, flow rate, concentration, and time. d. Plot the concentration of salt as a function of time for the described case. Now substitute the numbers you were given. Hint: you can use Excel or another helpful plotting tool. e. Calculate how long it takes before the concentration in the lake has dropped below 100 mg/L. f. If the inlet to the lake is increased to 1500 m³ per hour, how does this change your g. result? Describe or plot the results for this situation in comparison to the base case of 1000 m³ flow. How long does it take to get below 100 mg/L in this situation? When we let go of our assumption of the lake behaving like an ideally stirred tank reactor, what do you expect to happen? Describe and give reasoning.

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a To write a general mass balance for the total amount of water in the lake we can consider the inflow and outflow rates of water Inflow rate 1000 mhr Outflow rate 1000 mhr The mass balance equation c... View the full answer