A seawater pumping station is to pump X ton/hour of seawater with a relative density, RD). If it is desired that the velocity in the intake pipe to the pump will not exceed v1 cm/s, and the velocity in the outlet pipe is not to exceed v2 cm/s. Where,X = 29 ton/hour RD = 1.21 v1 = 27 cm/sv2 = 50 cm/s1 Tonne (Ton) =1000 kgDetermine suitable inlet pipe radius in mm.
Question
A seawater pumping station is to pump X ton/hour of seawater with a relative density, RD). If it is desired that the velocity in the intake pipe to the pump will not exceed v1 cm/s, and the velocity in the outlet pipe is not to exceed v2 cm/s. Where,X = 29 ton/hour RD = 1.21 v1 = 27 cm/sv2 = 50 cm/s1 Tonne (Ton) =1000 kgDetermine suitable inlet pipe radius in mm.
Solution
To find the suitable inlet pipe radius, we first need to convert the given values into appropriate units.
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Convert the flow rate from ton/hour to kg/s: X = 29 ton/hour = 29 * 1000 kg/hour = 29000 kg/hour Since 1 hour = 3600 seconds, X = 29000 kg/hour = 29000/3600 kg/s = 8.056 kg/s
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Convert the velocity from cm/s to m/s: v1 = 27 cm/s = 27/100 m/s = 0.27 m/s
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Use the formula for flow rate (Q) which is Q = velocity (v) * area (A). We can rearrange this to solve for area: A = Q/v.
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Substitute the values into the formula: A = 8.056 kg/s / 0.27 m/s = 29.83 m²/s
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The area of a pipe is given by the formula A = πr², where r is the radius. We can rearrange this to solve for r: r = sqrt(A/π).
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Substitute the value into the formula: r = sqrt(29.83/π) = 3.08 m
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Convert the radius from m to mm: r = 3.08 m = 3.08 * 1000 mm = 3080 mm
So, the suitable inlet pipe radius is approximately 3080 mm.
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