The dimensionless number defined by the ratio of inertial force to viscous force is called
Show Hint
- Mach number
- Froude number
- Weber number
- Reynolds number
The Correct Option is D
Solution and Explanation
- \( \rho \) is the fluid density,
- \( v \) is the velocity of the fluid,
- \( L \) is a characteristic length,
- \( \mu \) is the dynamic viscosity.
The Reynolds number helps determine whether the flow will be laminar or turbulent:
- Low Reynolds numbers (\( Re<2000 \)) indicate laminar flow,
- High Reynolds numbers (\( Re>4000 \)) indicate turbulent flow.
Thus, the correct answer is (D) Reynolds number. Final Answer: (D) Reynolds number
Top Questions on Fluid Mechanics
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).
GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]- Water flows through a horizontal pipe with a velocity of 2 m/s. The cross-sectional area of the pipe reduces to half. What is the velocity of water in the narrower section?
- BITSAT - 2025
- Physics
- Fluid Mechanics
- Consider the flowsheet in the figure for manufacturing C via the reaction \( A + B \rightarrow C \) in an isothermal CSTR. The split in the separator is perfect so that the recycle stream is free of C and the product stream is pure C. Let \( x_i \) denote the mole fraction of species \( i \) (where \( i = A, B, C \)) in the CSTR, which is operated in excess B with \( x_B/x_A = 4 \). The reaction is first-order in A with the reaction rate \( (-r_A) = k x_A \), where \( k_x = 5.0 \, {kmol}/({m}^3 \cdot {h}) \). The reactor volume \( V \) in \( {m}^3 \) is to be optimized to minimize the cost objective \( J = V + 0.25 R \), where \( R \) is the recycle rate in \( {kmol/h} \). For a product rate \( P = 100 \, {kmol/h} \), the optimum value of \( V \) is ____ \( {m}^3 \) (rounded off to the nearest integer). Given: \[ \frac{d}{dz} \left( \frac{z}{(1-z)^2} \right) = \frac{1}{(1 - 2z)^2} \]
- An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg°C). Assuming water is incompressible with a density of 1000 kg/m³, the maximum temperature rise of water across the pump is \_\_\_\_°C (rounded off to 3 decimal places).
Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?
Questions Asked in GATE PI exam
Courage : Bravery :: Yearning :
Select the most appropriate option to complete the analogy.In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
- In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723°C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950°C to below 723°C, the fraction of eutectoid ferrite is .............
- GATE PI - 2025
- Static Equilibrium
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?
