The Grashoff number is expressed as________________?
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Answer: A. gD3.β.Δtρ2/μ2
Explanation
The Grashoff number represents the dimensionless ratio of buoyancy forces to viscous forces. Its mathematical formulation incorporates gravitational acceleration, volumetric expansion, and temperature difference. Dynamic viscosity squared and density squared correctly populate the denominator of the expression. Dimensionless numbers simplify the analysis of heat transfer and fluid mechanics problems. Buoyancy forces drive natural convection currents in stagnant or slowly moving fluid environments. Fluid properties vary with temperature, influencing the magnitude of the calculated Grashoff number.
Calculating the Grashoff number is essential for determining heat transfer coefficients in natural convection. Engineers use this parameter in correlations for vertical plates, cylinders, and enclosed spaces. Thermal design of electronic enclosures often relies on natural convection dimensionless groupings. The remaining options feature incorrect exponents and variable arrangements for viscosity and density. Incorrectly placed pressure or velocity terms violate the dimensional homogeneity of the ratio. Altered exponent configurations fail to represent the physical balance of buoyancy and viscous forces.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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