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Understand Bernoulli's Principle and its application in relating pressure, kinetic energy per unit volume, and potential energy per unit volume in streamline flow.
Calculate fluid dynamics using the Equation of Continuity, ensuring the product of cross-sectional area and velocity remains constant in incompressible fluid flow.
Apply Pascal's Law to determine pressure transmission in enclosed fluids and its applications in hydraulic systems.
Analyze the viscous drag force on spheres using Stokes' Law and its dependence on radius, velocity, and fluid viscosity.
Explore the concept of Surface Tension as a force per unit length at the liquid interface and its implications in various phenomena.
Investigate Capillary Action and the factors influencing the rise or fall of liquids in narrow tubes.
Derive the Pressure Variation with Depth formula and apply it to calculate pressure changes in fluids due to depth.
Examine the concept of Viscosity and its role in fluid resistance to deformation or flow.
Evaluate Dynamic Lift and the Magnus Effect in the context of lift forces on bodies moving through fluids.
Utilize Torricelli's Law to determine the speed of efflux of fluids under gravity from an orifice.
Define and calculate Pressure, Density, and Relative Density, and apply these concepts in numerical problems.
Differentiate between Atmospheric Pressure, Gauge Pressure, and use a Manometer for pressure-difference calculations.
Apply Pascal's Law in Hydraulic Machines to understand mechanical advantage and force transmission.
Distinguish between Streamline, Laminar, and Turbulent Flow, and understand the significance of critical speed.
Calculate Terminal Velocity using Stokes' Law and analyze the effects of buoyancy and density differences.
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Definition: Relates pressure, kinetic energy per unit volume, and potential energy per unit volume in a streamline flow, stating their sum remains constant.
Equation: P+21ρv2+ρgh=constant
Assumptions: Applies to incompressible, non-viscous fluids in steady flow.
Applications: Explains phenomena like lift on airplane wings and the functioning of carburetors.
Equation of Continuity
Definition: For incompressible fluid flow, the product of cross-sectional area and velocity remains constant along a streamline.
Equation: A1v1=A2v2
Conservation: Represents conservation of mass in fluid dynamics.
Pascal's Law
Statement: Pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel.
Applications: Basis for hydraulic lifts and hydraulic brakes.
Stokes' Law
Definition: Describes the viscous drag force on a sphere moving through a fluid.
Equation: F=6πηav
Variables:
η: Viscosity of the fluid
a: Radius of the sphere
v: Velocity of the sphere
Surface Tension
Definition: The force per unit length acting at the interface between a liquid and another medium.
Equation: Surface tension S=2lF
Phenomena: Explains capillary action and the formation of droplets.
Capillary Action
Definition: The rise or fall of a liquid in a narrow tube due to surface tension and adhesive forces.
Equation: h=ρga2Scosθ
Variables:
h: Height of the liquid column
S: Surface tension
θ: Contact angle
ρ: Density of the liquid
a: Radius of the tube
Pressure Variation with Depth
Equation: P=Pa+ρgh
Explanation: Pressure in a fluid increases with depth due to the weight of the fluid above.
Viscosity
Definition: A measure of a fluid's resistance to deformation or flow.
Equation: η=AFvl
Units: Poiseuille (Pl), N s m⁻², or Pa s
Dynamic Lift and Magnus Effect
Dynamic Lift: Force on a body moving through a fluid due to pressure differences.
Magnus Effect: Lift force on a spinning object due to differences in velocity and pressure.
Torricelli's Law
Definition: Describes the speed of efflux of a fluid under gravity from an orifice.
Equation: v=2gh
Pressure, Density and Relative Density
Pressure: P=AF
Density: ρ=Vm
Relative Density: Ratio of the density of a substance to the density of a reference substance.
Atmospheric Pressure, Gauge Pressure and Manometer
Atmospheric Pressure: Pressure exerted by the weight of the atmosphere.
Gauge Pressure: Difference between absolute pressure and atmospheric pressure.
Manometer: Device for measuring pressure differences.
Hydraulic Machines
Principle: Based on Pascal's law.
Examples: Hydraulic lift and hydraulic brakes.
Streamline, Laminar and Turbulent Flow
Streamline Flow: Flow where each particle follows a smooth path.
Laminar Flow: Smooth, orderly fluid motion.
Turbulent Flow: Chaotic, irregular fluid motion.
Terminal Velocity
Definition: The constant velocity reached by a sphere falling through a viscous medium.
Equation: vt=9η2a2(ρ−σ)g
Variables:
vt: Terminal velocity
a: Radius of the sphere
ρ: Density of the sphere
σ: Density of the fluid
g: Acceleration due to gravity
η: Viscosity of the fluid
This chapter covers the mechanical properties of fluids, focusing on principles such as Bernoulli's principle, Pascal's law, and the equation of continuity, which are fundamental to understanding fluid dynamics and applications in real-world scenarios.
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The product of cross-sectional area and velocity remains constant.
B.
The pressure remains constant along a streamline.
C.
The density of the fluid changes with velocity.
D.
The flow rate is inversely proportional to the cross-sectional area.
Correct Answer: A
Solution:
The equation of continuity for incompressible fluid flow states that the product of cross-sectional area and velocity remains constant along a streamline.
Chapter Concept:
Equation of Continuity
A.
150 N
B.
450 N
C.
900 N
D.
50 N
Correct Answer: B
Solution:
The force exerted by the wheel cylinder can be calculated using the area ratio: F2=F1×(d1d2)2=50×(13)2=450 N.
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True or False
Correct Answer: True
Solution:
The Magnus effect occurs when a spinning ball drags air along with it, creating a pressure difference due to varying velocities of air above and below the ball, resulting in a net force that causes deviation.
Chapter Concept :
Dynamic Lift and Magnus Effect
Correct Answer: True
Solution:
Bernoulli's principle is a statement of the conservation of energy for fluid motion, indicating that the total mechanical energy is conserved in a streamline flow.
Chapter Concept :
Bernoulli's Principle
Chapter Concept:
Hydraulic Machines
A.
Gravitational forces
B.
Adhesive forces between the liquid and tube material
C.
Cohesive forces within the liquid
D.
External pressure applied on the liquid
Correct Answer: B
Solution:
Capillary action is caused by adhesive forces between the liquid and the tube material, along with surface tension.
Chapter Concept:
Capillary Action
A.
100 N
B.
1000 N
C.
10 N
D.
10000 N
Correct Answer: B
Solution:
According to Pascal's Law, the pressure applied to the first piston is transmitted undiminished to the second piston. Therefore, P1=P2, which implies A1F1=A2F2. Solving for F2, we get F2=F1×A1A2=100N×0.01m20.1m2=1000N.
Chapter Concept:
Pascal's Law
A.
1.01×105 Pa
B.
1.03×105 Pa
C.
1.28×105 Pa
D.
1.33×105 Pa
Correct Answer: C
Solution:
The pressure difference due to mercury is ΔP=ρgh=13.6×103×9.8×0.2=2.67×104 Pa. Therefore, the absolute pressure of the gas is P=Pa+ΔP=1.01×105+2.67×104=1.28×105 Pa.
Chapter Concept:
Atmospheric Pressure, Gauge Pressure and Manometer
A.
290.8 Pa
B.
145.4 Pa
C.
72.7 Pa
D.
36.35 Pa
Correct Answer: A
Solution:
The pressure difference across a spherical drop is given by ΔP=r2S, where S is the surface tension and r is the radius. Substituting the given values, ΔP=0.00052×0.0727=290.8 Pa.
Chapter Concept:
Pascal's Law
A.
A1V1=A2V2
B.
A1V12=A2V22
C.
A12V1=A22V2
D.
A1V13=A2V23
Correct Answer: A
Solution:
The principle of continuity for incompressible fluid flow states that the product of cross-sectional area and velocity remains constant along the pipe: A1V1=A2V2.
Chapter Concept:
Streamline, Laminar and Turbulent Flow
A.
Increasing the radius of the sphere
B.
Decreasing the viscosity of the fluid
C.
Reducing the velocity of the sphere
D.
Decreasing the density of the sphere
Correct Answer: A
Solution:
According to Stokes' Law, the drag force F is directly proportional to the radius a, the viscosity η, and the velocity v. Increasing the radius of the sphere will increase the drag force.
Chapter Concept:
Stokes' Law
A.
The sum of pressure, kinetic energy per unit volume, and potential energy per unit volume
B.
The sum of pressure and temperature
C.
The sum of kinetic energy and temperature
D.
The sum of potential energy and temperature
Correct Answer: A
Solution:
Bernoulli's principle states that the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline.
Chapter Concept:
Bernoulli's Principle
A.
0.148 m
B.
0.074 m
C.
0.037 m
D.
0.296 m
Correct Answer: A
Solution:
The height of capillary rise is given by h=ρga2ScosΘ. With Θ=0, cosΘ=1. Substituting the given values, h=1000×9.8×0.00052×0.0727=0.148 m.
Chapter Concept:
Pascal's Law
Correct Answer: True
Solution:
The equation P=Pa+ρgh accurately describes how pressure increases with depth in a fluid due to the weight of the fluid above. Pa represents the atmospheric pressure at the surface, ρ is the density of the fluid, g is the gravitational acceleration, and h is the depth below the surface.
Chapter Concept :
Pressure Variation with Depth
Correct Answer: True
Solution:
The pressure in a fluid indeed increases with depth because of the weight of the fluid above, as described by the equation P=Pa+ρgh, where Pa is the atmospheric pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the depth.
Chapter Concept :
Pressure Variation with Depth
Correct Answer: True
Solution:
The Magnus effect describes how a spinning ball creates a pressure difference due to varying velocities of air around it, resulting in a lift force.
Chapter Concept :
Dynamic Lift and Magnus Effect
Correct Answer: True
Solution:
Torricelli's Law states that the speed of efflux of a fluid from an orifice is the same as the speed of a freely falling body from the same height.
Chapter Concept :
Torricelli's Law
Correct Answer: True
Solution:
Stokes' law describes the viscous drag force on a sphere moving through a fluid as being proportional to the sphere's radius, velocity, and the fluid's viscosity.
Chapter Concept :
Stokes' Law
Correct Answer: True
Solution:
Capillary action is a result of surface tension and adhesive forces between the liquid and the tube material, which creates a pressure difference across the curved liquid-air interface, causing the liquid to rise.
Chapter Concept :
Capillary Action
Correct Answer: True
Solution:
The pressure inside a spherical drop is greater than the pressure outside because the surface tension causes a pressure difference across the liquid-air interface, as described by the equation (Pi−Po)=r2S where S is the surface tension and r is the radius of the drop.
Chapter Concept :
Atmospheric Pressure, Gauge Pressure and Manometer
Correct Answer: False
Solution:
Streamlines cannot cross each other in a steady flow because if they did, a fluid particle at the intersection would have two different velocities, which is not possible.
