GATE 2023 AG – Question 34

Dairy and Food Engineering · Unit Operations in Dairy and Food Engineering · 1 mark · Numerical answer

A basket centrifuge rotates1000 rpm. Lighter-liquid surface and interface radii are.1025,.105 m. Light/heavy densities are920,1015 kg/m³. Find radial pressure difference maintaining the interface, in kPa, to three decimals;use π=3.14.

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Correct answer: 2.610 to 2.620

Explanation

In the lighter-liquid layer, radial equilibrium gives $dp/dr=\rho_l\omega^2r$. Integrate from its surface to interface: $\Delta p=\frac12\rho_l\omega^2(r_i^2-r_l^2)$. With $\omega=2(3.14)(1000)/60$,this is 2.614163 kPa, rounded **2.614 kPa**. Only the light-fluid density is used across this specified light layer; the heavy density is extraneous to this pressure increment.

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