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Statement-1: For reynold number R(e)gt20...

Statement-1: For reynold number `R_(e)gt2000` the flow of fluid is turbulent.
Statement-2: Inertial forces are dominant compared to the viscous forces at such high reynold numbers.

A

If both assertion and reason are true and reason is the correct explanation of assertion

B

If both assertion and reason are true but reason is not the correct explanation of assertion

C

If assertion is true but reason is false

D

If both assertion and reason are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze both statements regarding the Reynolds number and its implications on fluid flow. ### Step-by-Step Solution: 1. **Understanding Reynolds Number (Re)**: The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined as: \[ R_e = \frac{\rho v d}{\mu} \] where: - \( \rho \) = density of the fluid - \( v \) = velocity of the fluid - \( d \) = characteristic length (typically diameter of the pipe) - \( \mu \) = dynamic viscosity of the fluid 2. **Analyzing Statement 1**: Statement 1 claims that for \( R_e > 2000 \), the flow of fluid is turbulent. This is a well-established criterion in fluid mechanics. When the Reynolds number exceeds 2000, the flow transitions from laminar to turbulent. Therefore, Statement 1 is **correct**. 3. **Analyzing Statement 2**: Statement 2 states that inertial forces are dominant compared to viscous forces at high Reynolds numbers. The Reynolds number is essentially a ratio of inertial forces to viscous forces: \[ R_e = \frac{\text{Inertial Forces}}{\text{Viscous Forces}} \] When \( R_e \) is greater than 2000, it indicates that inertial forces significantly outweigh viscous forces, leading to turbulent flow. Thus, Statement 2 is also **correct**. 4. **Conclusion**: Since both statements are correct and Statement 2 provides a valid explanation for Statement 1, we conclude that both statements are true and Statement 2 explains Statement 1. ### Final Answer: Both Statement 1 and Statement 2 are correct, and Statement 2 is the correct explanation for Statement 1.

To solve the problem, we need to analyze both statements regarding the Reynolds number and its implications on fluid flow. ### Step-by-Step Solution: 1. **Understanding Reynolds Number (Re)**: The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined as: \[ R_e = \frac{\rho v d}{\mu} ...
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Knowledge Check

  • For turbulent flow, the value of Reynolds number is

    A
    1. `R_(e)gt 2000`
    B
    2. `R_(e) lt 2000`
    C
    3. `1000ltR_(e)lt2000`
    D
    4. `R_(e) = 1000`
  • Assertion: The flow is turbulent for Reynolds number greater than 2000 Reason: Turbulence dissipates kinetic energy in the form of heat.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true and reason is false.
    D
    If both assertion and reason are false.
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