Experimentation is required for the simplest flow cases
Newton’s law of viscosity applies
The fluid particles move in irregular and haphazard path
Viscosity is unimportant
Answer (Detailed Solution Below)
Option 2 : Newton’s law of viscosity applies
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Laminar and Turbulent Flow MCQ Question 1 Detailed Solution
Turbulent flow is the random, disordered and dis-organised flow which has bulk and or macroscopic mixing. It occurs at higher flow velocities compared to laminar flow. In turbulent flow, inertia forces are significant as compared to viscous forces.
For flow in the pipes if Reynold's number is less than 2000 the flow is called the laminar and if it is more than 4000, the flow is called turbulent flow. If the Reynolds number lies between 2000 and 4000 the flow may be laminar or turbulent ( also known as transition period).
A steady, incompressible, two-dimensional velocity field is given by, \(\vec V = \left( {u,v} \right) = \left( {0.5 + 0.8x} \right)\hat i + \left( {1.5 - 0.8y} \right)\hat j\) The number of stagnation points there in the flow field is
Zero
Many
1
2
Answer (Detailed Solution Below)
Option 3 : 1
Laminar and Turbulent Flow MCQ Question 4 Detailed Solution
A stagnation point is a point in a flow field where the local velocity of the fluid is zero.
The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. Because all the velocity head is converted into the pressure head at the stagnation point.
This static pressure is called the stagnation pressure.
For the Stagnation point, velocity should be zero.
Calculation:
Given:
\(\vec V = \left( {u,v} \right) = \left( {0.5 + 0.8x} \right)\hat i + \left( {1.5 - 0.8y} \right)\hat j\)
So u = 0 & v = 0
⇒ 0.5 + 0.8x = 0 ⇒ x = -0.625
⇒ 1.5 - 0.8y = 0 ⇒ y = 1.875
So only one value for (x, y) i.e. (-0.625, 1.875).
Turbulent flow is the random, disordered and dis-organised flow which has bulk and or macroscopic mixing. It occurs at higher flow velocities compared to laminar flow. In turbulent flow, inertia forces are significant as compared to viscous forces.
For flow in the pipes if Reynold's number is less than 2000 the flow is called the laminar and if it is more than 4000, the flow is called turbulent flow. If the Reynolds number lies between 2000 and 4000 the flow may be laminar or turbulent ( also known as transition period).
Turbulent flow is the random, disordered and dis-organised flow which has bulk and or macroscopic mixing. It occurs at higher flow velocities compared to laminar flow. In turbulent flow, inertia forces are significant as compared to viscous forces.
For flow in the pipes if Reynold's number is less than 2000 the flow is called the laminar and if it is more than 4000, the flow is called turbulent flow. If the Reynolds number lies between 2000 and 4000 the flow may be laminar or turbulent ( also known as transition period).
The flow rate through a pipe is usually measured by providing a coaxial area contraction within the pipe and by recording the pressure drop across the contraction, which is the application of Bernoulli’s equation.
Bernoulli's principle can be derived from the principle of conservation of energy.
The Bernoulli's theorem states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline
Bernoulli equation represented in head form (the total energy per unit weight):
\(\frac{P}{\rho g} + \frac{{{v^2}}}{{2g}} + Z = Constant\)
Three flow meters primarily operate on this principle:
Pitot tube
Venturimeter
Orifice meter
Moment of momentum equation
Impulse (J): It is defined as the integral of force with respect to time. It is a vector quantity It is also defined as a change in the linear moment (P) with respect to time.
J = F × dt = ΔP
According to Newton's second law, the force can be defined as a moment per time.
A cricket player lowers his hands while catching the ball. By doing so the duration (time) of impact increases and hence the effect of force decreases.
When a person falls from a certain height on the floor, he receives more injuries as compared to falling on a heap of sand. It is because of increasing the time of impact hence decreasing the impact of force.
Continuity Equation
It is based on the principle of conservation of mass.
For a fluid flowing through a pipe at all the cross-section, the quantity of fluid per second is constant.
The continuity equation is given as \({\rho _1}{A_1}{V_1} = \;{\rho _2}{A_2}{V_2}\)
The continuity equation applies to all fluids, compressible and incompressible flow, Newtonian and non-Newtonian fluids. It expresses the law of conservation of mass at each point in a fluid and must, therefore, be satisfied at every point in a flow field. Hence continuity equation relates the mass flow rate along the streamline.
The continuity equation is connected with the conservation of mass and it can be applied to viscous/non-viscous, the compressibility of the fluid, or the steady/unsteady flow.
A steady, incompressible, two-dimensional velocity field is given by, \(\vec V = \left( {u,v} \right) = \left( {0.5 + 0.8x} \right)\hat i + \left( {1.5 - 0.8y} \right)\hat j\) The number of stagnation points there in the flow field is
Zero
Many
1
2
Answer (Detailed Solution Below)
Option 3 : 1
Laminar and Turbulent Flow MCQ Question 10 Detailed Solution
A stagnation point is a point in a flow field where the local velocity of the fluid is zero.
The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. Because all the velocity head is converted into the pressure head at the stagnation point.
This static pressure is called the stagnation pressure.
For the Stagnation point, velocity should be zero.
Calculation:
Given:
\(\vec V = \left( {u,v} \right) = \left( {0.5 + 0.8x} \right)\hat i + \left( {1.5 - 0.8y} \right)\hat j\)
So u = 0 & v = 0
⇒ 0.5 + 0.8x = 0 ⇒ x = -0.625
⇒ 1.5 - 0.8y = 0 ⇒ y = 1.875
So only one value for (x, y) i.e. (-0.625, 1.875).