Question:
Weber number is the ratio of
Weber number is the ratio of
Show Hint
Quick Fluid Mechanics Reference Summary Table:
- Reynolds Number (\(Re\)) = Inertia / Viscous
- Froude Number (\(Fr\)) = Inertia / Gravity
- Weber Number (\(We\)) = Inertia / Surface Tension
- Mach Number (\(M\)) = Inertia / Elasticity
Updated On: Jul 4, 2026
- Surface tension forces to pressure forces
- Inertial forces to Surface tension forces
- Pressure forces to viscous forces
- Viscous forces to gravity forces
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
In fluid mechanics, dimensionless numbers are used to analyze fluid behavior, design scale-model experiments, and characterize flow regimes. These numbers represent ratios of different forces acting within the fluid system.
The Weber number (\(We\)) is a dimensionless parameter that measures the relative importance of fluid inertia compared to its surface tension forces. It is useful when analyzing multiphase flows, fluid interfaces, bubble formation, droplet breakup, and thin-film flows.
Step 1: Formulating the mathematical expressions for the forces.
Let us look at the physical formulas for inertial and surface tension forces to see how the Weber number is derived:
• Inertial Force: Generates momentum from fluid mass and motion, expressed as: \[ F_{\text{inertia}} \propto \rho \cdot v^2 \cdot L^2 \]
• Surface Tension Force: Acts along fluid interfaces to minimize surface area, expressed as: \[ F_{\text{surface tension}} \propto \sigma \cdot L \]
Where \(\rho\) is fluid density, \(v\) is flow velocity, \(L\) is a characteristic length scale, and \(\sigma\) is the surface tension coefficient.
Step 2: Taking the ratio to define the Weber number.
Dividing the inertial force by the surface tension force yields the standard expression for the Weber number: \[ We = \frac{\text{Inertial Forces}}{\text{Surface Tension Forces}} = \frac{\rho \cdot v^2 \cdot L^2}{\sigma \cdot L} = \frac{\rho \cdot v^2 \cdot L}{\sigma} \] This ratio shows how intensely a gas or liquid stream disrupts an interface relative to the stabilizing cohesive force of surface tension.
Step 3: Confirming the correct option option tag.
Since the Weber number is defined as the direct ratio of inertial forces to surface tension forces, it matches Option (B).
Step 1: Formulating the mathematical expressions for the forces.
Let us look at the physical formulas for inertial and surface tension forces to see how the Weber number is derived:
• Inertial Force: Generates momentum from fluid mass and motion, expressed as: \[ F_{\text{inertia}} \propto \rho \cdot v^2 \cdot L^2 \]
• Surface Tension Force: Acts along fluid interfaces to minimize surface area, expressed as: \[ F_{\text{surface tension}} \propto \sigma \cdot L \]
Where \(\rho\) is fluid density, \(v\) is flow velocity, \(L\) is a characteristic length scale, and \(\sigma\) is the surface tension coefficient.
Step 2: Taking the ratio to define the Weber number.
Dividing the inertial force by the surface tension force yields the standard expression for the Weber number: \[ We = \frac{\text{Inertial Forces}}{\text{Surface Tension Forces}} = \frac{\rho \cdot v^2 \cdot L^2}{\sigma \cdot L} = \frac{\rho \cdot v^2 \cdot L}{\sigma} \] This ratio shows how intensely a gas or liquid stream disrupts an interface relative to the stabilizing cohesive force of surface tension.
Step 3: Confirming the correct option option tag.
Since the Weber number is defined as the direct ratio of inertial forces to surface tension forces, it matches Option (B).
Was this answer helpful?
0
0
Top TS PGECET Chemical Engineering Questions
- The degrees of freedom for a system consisting a gaseous mixture of \( N_2 \), \( H_2 \), and \( NH_3 \) is
- A bypass stream in a chemical process is useful, because it
- Sometimes in chemical processes, a part of the outlet stream is rejected as waste in order to keep the impurity level in the system within limits. This phenomenon is termed as
- In a chemical reaction the material balance calculation is based on
- The substance that appears in one incoming stream and outgoing stream which serves as reference for computations is called as a
View More Questions
Top TS PGECET Fluid Mechanics Questions
- Potential flow is the flow of
- Newton’s law of viscosity relates
- Dimensions of kinematic viscosity is
- The loss due to sudden contraction is proportional to
- For Non-Newtonian fluids, power law model consists parameter \( K \) known as
View More Questions
Top TS PGECET Questions
- If \( P = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix} \) is the modal matrix of \( A = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{pmatrix} \) then the sum of all the elements of \( P^{-1}AP \) is
- If the system of equations \( kx + y + z = k - 1 \), \( x + ky + z = k - 1 \), and \( x + y + kz = k - 1 \) has infinite solutions, then \( k \) is
- The value of the integral \( \int_C (2xy - x^2) \, dx + (x^2 + y^2) \, dy \) where \( C \) is the boundary of the region enclosed by \( y = x^2 \) and \( y^2 = x \), described in the positive sense, is
- Let \( f(x) = \log x \). The number \( C \) strictly between \( e^2 \) and \( e^3 \) such that its reciprocal is equal to \( \frac{f(e^3) - f(e^2)}{e^3 - e^2} \) is
- The solution of the differential equation \( (D^2 + 2)y = x^2 \) is
View More Questions