GATE 2023 AG – Question 35

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

Milk in a homogenizer drops from 250 to 10 bar. Density is 1030 kg/m³. Neglect losses and upstream kinetic energy. Find valve exit speed in m/s, to three decimals.

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Correct answer: 215.850 to 215.900

Explanation

Bernoulli conversion of pressure energy to kinetic energy gives $v=\sqrt{2\Delta p/\rho}$. Pressure drop is 240 bar=$24\times10^6$ Pa. Thus $v=\sqrt{48\times10^6/1030}=215.874829$ m/s, rounded **215.875 m/s**. This is the ideal velocity implied by the supplied pressure-drop calculation.

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