Suggested Response - Q4

**A whirlpool is connected to a cast-out pump, with an NPSHR of 2 m water, using a suction line of length 10 m with a linear pressure drop of 0.75 kPa/m. If the wort has a vapour pressure of 90 kPa a, what would the required value be of the vertical head between the whirlpool outlet and the pump inlet to ensure the pump does not cavitate?

Wort density is 1,060 kg/m3, and atmospheric pressure is 100 kPa.

Response:

We can represent the problem in a diagram:

SAQ4

In order for the pump to operate safely, i.e. without cavitating, we require NPSHA ≥ NPSHR:

N P S H subscript A greater or equal than 2 m space w a t e r

NPSHA is given by:

N P S H subscript A equals left parenthesis H subscript S u c t i o n end subscript minus H subscript V a p o u r end subscript right parenthesis

Where the pump suction head, HSuction, is given by:

H subscript S u c t i o n end subscript equals H subscript A t m o s p h e r i c end subscript plus H subscript H y d r o s t a t i c end subscript minus increment H subscript l o s t end subscript

N P S H subscript A equals left parenthesis H subscript A t m o s p h e r i c end subscript plus H subscript H y d r o s t a t i c end subscript minus increment H subscript l o s t end subscript minus H subscript V a p o u r end subscript right parenthesis

Hence:

left parenthesis H subscript A t m o s p h e r i c end subscript plus H subscript H y d r o s t a t i c end subscript minus increment H subscript l o s t end subscript minus H subscript V a p o u r end subscript right parenthesis greater or equal than 2 m space w a t e r

We must be careful here as some of the head values are in metres of wort and water, and as the densities of these liquids are different, the heads are not directly comparable. So let us convert everything into pressures:

left parenthesis 100 cross times 10 cubed plus H cross times 1 comma 060 cross times 9.81 minus 10 cross times 0.75 cross times 10 cubed minus 90 cross times 10 cubed right parenthesis greater or equal than 2 cross times 1 comma 000 cross times 9.81

It should be noted that H, the hydrostatic head between the base of the whirlpool and the pump suction, is the unknown.

left parenthesis 100 cross times 10 cubed plus H cross times 10.4 cross times 10 cubed minus 7.5 cross times 10 cubed minus 90 cross times 10 cubed right parenthesis greater or equal than 19.6 cross times 10 cubed

H greater or equal than fraction numerator 17.1 cross times 10 cubed over denominator 10.4 cross times 10 cubed end fraction

H greater or equal than 1.64 space m

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