Choose the CORRECT option for pathlines, streaklines and streamlines for a STEADY flow field.
Show Hint
- All three lines are identical
- Only pathlines and streaklines are identical
- Only pathlines and streamlines are identical
- Only streamlines and streaklines are identical
The Correct Option is A
Solution and Explanation
Step 1: Define Each Line Type.
Pathlines: the trajectory that individual fluid particles follow.
Streamlines: lines that are tangent to the velocity vector of the flow at every point.
Streaklines: the locus of particles that have passed sequentially through a particular point.
Step 2: Relationship in Steady Flow.
In a steady flow, where the flow properties at any point do not change over time, pathlines, streaklines, and streamlines coincide.
Top Questions on Fluid Mechanics
- Consider a velocity field \( \vec{V} = 3z \hat{i} + 0 \hat{j} + Cx \hat{k} \), where \( C \) is a constant. If the flow is irrotational, the value of \( C \) is (rounded off to 1 decimal place).
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?
- For a fully-developed pipe flow, which of the following options is/are correct?
A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m\(^{-3}\) while the density of water is 1000 kg m\(^{-3}\). For the manometer reading of \( h = 30 \) mm of mercury, the speed of air in the wind tunnel is _________ m s\(^{-1}\) (rounded off to 1 decimal place).
- An oil of density \(870 \, {kg/m}^3\) and viscosity \(0.036 \, {Pa.s}\) flows through a straight pipe of 10 cm diameter and 1.5 km length at the flow rate of 250 liters per minute under the steady and incompressible flow conditions.
To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is \(11.60 \, {m}\). Using gravitational acceleration as \(10 \, {m/s}^2\), the minor head loss contributed by the presence of the valve in m {(rounded off to 2 decimal places) is ..........}- GATE XE - 2025
- Engineering Sciences
- Fluid Mechanics
Questions Asked in GATE CH exam
An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring as shown in the figure. The piston is frictionless and massless. The spring constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the final equilibrium temperature of the gas is __________ K (rounded off to the nearest integer).
- GATE CH - 2025
- Thermodynamics
- Consider the matrix: \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix} \] The eigenvalues of the matrix are 0.27 and __________ (rounded off to 2 decimal places).
- GATE CH - 2025
- Linear Algebra
The residence-time distribution (RTD) function of a reactor (in min$^{-1}$) is
The mean residence time of the reactor is __________ min (rounded off to 2 decimal places).}- GATE CH - 2025
- Chemical Equations
Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is _________J/K (rounded off to 1 decimal place).
Given: Universal gas constant \( R = 8.314 \) J/(mol K), \( T_A = T_B = 273 \) K, \( P_A = P_B = 1 \) atm, \( V_B = 22.4 \) L, \( V_A = 3V_B \).- GATE CH - 2025
- Thermodynamics
The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is __________ MPa (rounded off to 3 decimal places).- GATE CH - 2025
- Thermodynamics