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A water treatment plant is required to process 28800 m3/d of raw water (density = 1000 kg/m3, kinematic viscosity = 10-6 m2/s). The rapid mixing tank imparts tank a velocity gradient of 900s-1 to blend 35 mg/l of alum with the flow for a detention time of 2 minutes. The power input (W) required for rapid mixing is
  • a)
    32.4
  • b)
    36
  • c)
    324
  • d)
    32400
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A water treatment plant is required to process 28800 m3/d of raw water...
Calculation of Power Input for Rapid Mixing

Given data:
Raw water flow rate = 28800 m3/d
Density of water = 1000 kg/m3
Kinematic viscosity of water = 10-6 m2/s
Velocity gradient = 900 s-1
Alum dosage = 35 mg/l
Detention time = 2 minutes

Step 1: Calculation of volumetric flow rate
Volumetric flow rate = Raw water flow rate / Density of water
Volumetric flow rate = 28800 m3/d / 1000 kg/m3
Volumetric flow rate = 28.8 m3/s

Step 2: Calculation of alum dosage in m3/s
Alum dosage = 35 mg/l
Alum dosage = 0.035 kg/m3
Mass flow rate of alum = Volumetric flow rate * Alum dosage
Mass flow rate of alum = 28.8 m3/s * 0.035 kg/m3
Mass flow rate of alum = 1.008 kg/s
Volume flow rate of alum = Mass flow rate of alum / Density of alum
Density of alum = 2330 kg/m3 (approx.)
Volume flow rate of alum = 1.008 kg/s / 2330 kg/m3
Volume flow rate of alum = 0.000432 m3/s

Step 3: Calculation of tank volume for rapid mixing
Detention time = 2 minutes = 120 seconds
Tank volume for rapid mixing = Volumetric flow rate * Detention time
Tank volume for rapid mixing = 28.8 m3/s * 120 s
Tank volume for rapid mixing = 3456 m3

Step 4: Calculation of power input for rapid mixing
Power input for rapid mixing = (Velocity gradient)3 * Density of water * Kinematic viscosity * Volume flow rate of alum * Tank volume for rapid mixing
Power input for rapid mixing = (900 s-1)3 * 1000 kg/m3 * 10-6 m2/s * 0.000432 m3/s * 3456 m3
Power input for rapid mixing = 32400 W

Therefore, the power input required for rapid mixing is 32400 W (Option D).
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A water treatment plant is required to process 28800 m3/d of raw water (density = 1000 kg/m3, kinematic viscosity = 10-6m2/s). The rapid mixing tank imparts tank a velocity gradient of 900s-1to blend 35 mg/l of alum with the flow for a detention time of 2 minutes. The power input (W) required for rapid mixing isa)32.4b)36c)324d)32400Correct answer is option 'D'. Can you explain this answer?
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