The upstream and downstream pressures in a homogenizer during homogenization of milk are maintained at 250 bar and 10 bar, respectively. If density of milk is 1030 kg m⁻³, then the velocity at which milk comes out of the homogenizing valve in m s⁻¹ is ________________________ (rounded off to 3 decimal places).
Official Answer Key:
215.850 to 215.900
Step-by-Step Solution & Explanation
Applying Bernoulli's equation across the homogenizing valve (converting pressure drop entirely to kinetic energy, as is standard for this idealized homogenizer-velocity calculation):
V = √(2ΔP/ρ) = √[2×(250−10)×10⁵ Pa / 1030 kg/m³] = √[2×240×10⁵/1030] = √(4,660,194) = 215.875 m/s. Within official range 215.850–215.900.
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