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Len [333]
3 years ago
14

In a sewage treatment plant, a large concrete tank initially contains 440,000 liters of liquid and 10,000 kg of fine suspended s

olids. To flush this material out of the tank, water is pumped into the vessel at a rate of 40,000 l/h. Liquid containing solids leaves at the same rate. Estimate the concentration of suspended solids in the tank at the end of 4 h. You can assume that the initial concentration of solids in the tank
Mathematics
1 answer:
viva [34]3 years ago
3 0

Answer:

Concentration = 8.26kg/m^3

Step-by-step explanation:

Given

  V = 440000L --- volume of tank

m = 10,000 kg --- solid mass

r = 40000L/hr --- outflow rate  

Required

Determine the concentration at the end of 4 hours

First, calculate the amount of liquid that has been replaced at the end of the 4 hours.

Amount = r * Time

Amount = 40000L/hr * 4hr

Amount = 40000L * 4

Amount = 160000L

This implies that, over the 4 hours; The tank has 160000 liters of liquid out of 440000 liters were replaced

Calculate the ratio of the liquid replaced.

Ratio = \frac{Amount}{Volume}

Ratio = \frac{160000L}{440000L}

Ratio = \frac{16}{44}

Ratio = \frac{4}{11}

Next, calculate the amount of solid left.

Amount (Solid)= Ratio * m

Amount (Solid)= \frac{4}{11} * 10000kg

Amount (Solid)= \frac{40000}{11}kg

Amount (Solid)= 3636kg

Lastly, the concentration is calculated as:

Concentration = \frac{Amount (Solid)}{Volume}

Concentration = \frac{3636kg}{440000L}

Convert L to cubic meters

Concentration = \frac{3636kg}{440000* 0.001m^3}

Concentration = \frac{3636kg}{440m^3}

Concentration = 8.26kg/m^3

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