Question:
Dimensionless parameter among the following options is
Dimensionless parameter among the following options is
Show Hint
Write the defining formula for each option and check whether the units cancel.
Updated On: Jul 16, 2026
- heat exchanger effectiveness
- humid heat of air-water vapour mixture
- humid volume of air-water vapour mixture
- overall heat transfer coefficient
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Check the units of each option.
Heat exchanger effectiveness is defined as the ratio of actual heat transfer rate to the maximum possible heat transfer rate, \(\varepsilon = \dfrac{Q_{actual}}{Q_{max}}\).
Both quantities in this ratio carry units of watts, so they cancel and effectiveness is a pure number.
Step 2: Rule out the other options.
Humid heat has units of \(\text{kJ.kg}^{-1}.\text{K}^{-1}\), humid volume has units of \(\text{m}^3.\text{kg}^{-1}\), and overall heat transfer coefficient has units of \(\text{W.m}^{-2}.\text{K}^{-1}\).
None of these three cancel out to a pure number, so all three carry dimensions.
Final Answer:
Only heat exchanger effectiveness is dimensionless. \[ \boxed{\text{heat exchanger effectiveness}} \]
Heat exchanger effectiveness is defined as the ratio of actual heat transfer rate to the maximum possible heat transfer rate, \(\varepsilon = \dfrac{Q_{actual}}{Q_{max}}\).
Both quantities in this ratio carry units of watts, so they cancel and effectiveness is a pure number.
Step 2: Rule out the other options.
Humid heat has units of \(\text{kJ.kg}^{-1}.\text{K}^{-1}\), humid volume has units of \(\text{m}^3.\text{kg}^{-1}\), and overall heat transfer coefficient has units of \(\text{W.m}^{-2}.\text{K}^{-1}\).
None of these three cancel out to a pure number, so all three carry dimensions.
Final Answer:
Only heat exchanger effectiveness is dimensionless. \[ \boxed{\text{heat exchanger effectiveness}} \]
Was this answer helpful?
0
0
Top GATE AG Dairy and Food Engineering Questions
- The condition of refrigerant at the exit of the compressor in a vapor compression refrigeration system is:
- If the diameter of fat globule in a cream separator is reduced to half and the rotational speed of the centrifuge increased to three times, the terminal settling velocity of fat globule is:
- The lighter liquid layer and the interphase layer in a basket centrifuge, rotating at a speed of 1000 rpm, are 0.1025 m and 0.105 m away from the center, respectively. Considering the densities of lighter and heavier liquids as 920 kg/m\(^3\) and 1015 kg/m\(^3\), the differential pressure in horizontal direction required to maintain the interphase layer in kPa is \underline{\hspace{3cm}} (rounded off to 3 decimal places, \(\pi = 3.14\)).
- 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 is \underline{\hspace{3cm}} (rounded off to 3 decimal places).
- The rotor shaft of an ice cream freezer consists of 3 scraper blades. The temperature difference between the ice cream mix and the refrigerant during freezing of ice cream is \(30^\circ C\). Density and latent heat of fusion of ice are 917 kg m\(^{-3}\) and 335 kJ kg\(^{-1}\), respectively. The overall heat transfer coefficient is 2000 kJ m\(^{-2}\) h\(^{-1}\) \(^{\circ}C^{-1}\). If the maximum thickness of ice formed before being scraped off is 10 μm, the minimum speed of the scraper shaft in rpm is:
View More Questions
Top GATE AG Heat and Mass Transfer in Food Processing Questions
- Specific heat, coefficient of viscosity, and thermal conductivity are related in the
- A 2 mm diameter electric wire is insulated with 2 mm thick plastic. The plastic has a thermal conductivity of \(0.5\ \text{W.m}^{-1}\text{.K}^{-1}\). The wire is exposed to air at 320 K and outside convective heat transfer coefficient is \(25\ \text{W.m}^{-2}\text{.K}^{-1}\). Wire surface temperature is constant at 420 K and remains unaffected by the covering. Assuming steady state heat transfer conditions, the ratio of heat loss per metre of wire length with insulation to that without insulation is nearest to (Take \(\pi = 3.14\))
Top GATE AG Questions
- If \(a\), \(b\), and \(c\) are the roots of \( 2x^3 - 3x^2 + px - 1 = 0 \) and the sum of two roots is 1, the value of \(p\) is:
- If the matrix \[ \begin{pmatrix} x & -3 \\ 2 & x - 5 \end{pmatrix} \] is singular, sum of the values of \( x \) is:
- The Laplace transform of \( \frac{s}{s^2 + a^2} \) is:
The equation \[ y'' + p(x)y' + q(x)y = r(x) \] is a _________ ordinary differential equation.
- The median of the following set of numbers: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138 is:
View More Questions