Find the best tutors and institutes for Class 11 Tuition
Q10.4(d):
Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
Solution :
Step 1: Theoretical Foundation of Fluid Momentum
To analyze the backward thrust experienced by a vessel with a small orifice, we apply the Principle of Conservation of Linear Momentum. According to Newton’s Second Law of Motion in terms of momentum, the force exerted by an object is proportional to the rate of change of its momentum, defined as:
$F = \frac{dp}{dt} = m \cdot \frac{dv}{dt}$ [Per Newton's Second Law]
When a fluid is at rest inside a closed vessel, the internal pressures exert equal and opposite forces on the walls of the vessel, resulting in a net force of zero. However, when an orifice is opened, the fluid at that point is no longer constrained by a wall, allowing it to accelerate out of the vessel.
Step 2: Derivation of the Efflux Force
Let $A$ be the area of the orifice and $v$ be the velocity of the fluid exiting the hole. According to Torricelli's Law, the velocity of efflux is given by $v = \sqrt{2gh}$, where $h$ is the height of the fluid column above the hole. The mass of the fluid exiting the vessel per unit time ($\frac{dm}{dt}$) is expressed as:
$\frac{dm}{dt} = \rho A v$
Where $\rho$ is the density of the fluid. The fluid gains momentum in the direction of the efflux. Since the initial momentum of the fluid was zero (relative to the vessel), the fluid undergoes a change in momentum given by $dp = (dm)v$.
Step 3: Applying Newton’s Third Law
The fluid exiting the vessel exerts a force on the exiting fluid stream to accelerate it. By Newton’s Third Law of Motion, for every action, there is an equal and opposite reaction. The fluid stream exerts a reaction force ($F_{thrust}$) on the vessel in the opposite direction of the velocity of the efflux.
The magnitude of this thrust is given by:
$F_{thrust} = v \cdot \frac{dm}{dt}$
Substituting $\frac{dm}{dt} = \rho A v$ into the equation:
$F_{thrust} = v (\rho A v) = \rho A v^2$
Substituting $v^2 = 2gh$ from Torricelli’s Law:
$F_{thrust} = \rho A (2gh) = 2 \rho A g h$
Visual Representation of Forces
Step 4: Conclusion
Because the symmetry of internal pressure is broken at the location of the hole, the pressure on the wall directly opposite to the hole remains, while the pressure at the hole is reduced to atmospheric pressure. The resulting unbalanced pressure differential, combined with the momentum change of the ejected mass, manifests as a backward recoil force on the vessel.
Final Solution: The backward thrust is a direct consequence of Newton's Third Law; as the vessel imparts momentum to the exiting fluid stream, the fluid exerts an equal and opposite reaction force on the vessel, expressed by the magnitude $F = 2 \rho A g h$.
More Questions from Class 11 Physics Mechanical Properties of Fluids EXERCISES
- Q9.1(a): Explain why (a) The blood pressure in humans is greater at the feet than at the brain
- Q9.1(b): Explain why (b) Atmospheric pressure at a height of about (6\text{ km}) decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than (100\text{ km})
- Q9.1(c): Explain why (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
- Q9.10: If (15.0\text{ cm}) of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = (13.6))
- Q9.11: Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain.
- Q9.12: Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation ? Explain.
- Q9.13: Glycerine flows steadily through a horizontal tube of length (1.5\text{ m}) and radius (1.0\text{ cm}). If the amount of glycerine collected per second at one end is (4.0 \times 10^{-3}\text{ kg s}^{-1}), what is the pressure difference between the two ends of the tube ? (Density of glycerine = (1.3 \times 10^{3}\text{ kg m}^{-3}) and viscosity of glycerine = (0.83\text{ Pa s})). [You may also like to check if the assumption of laminar flow in the tube is correct].
- Q9.14: In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are (70\text{ m s}^{-1})and (63\text{ m s}^{-1}) respectively. What is the lift on the wing if its area is (2.5\text{ m}^{2}) ? Take the density of air to be (1.3\text{ kg m}^{-3}).
- Q9.15: Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- Q9.16: The cylindrical tube of a spray pump has a cross-section of (8.0\text{ cm}^{2}) one end of which has (40) fine holes each of diameter (1.0\text{ mm}). If the liquid flow inside the tube is (1.5\text{ m min}^{-1}), what is the speed of ejection of the liquid through the holes ?
- Q9.17: A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of (1.5 \times 10^{-2}\text{ N}) (which includes the small weight of the slider). The length of the slider is (30\text{ cm}). What is the surface tension of the film ?
- Q9.18: Figure 9.21 (a) shows a thin liquid film supporting a small weight = (4.5 \times 10^{-2}\text{ N}). What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.
- Q9.19: What is the pressure inside the drop of mercury of radius (3.00\text{ mm}) at room temperature ? Surface tension of mercury at that temperature ((20^{\circ}\text{C})) is (4.65 \times 10^{-1}\text{ N m}^{-1}). The atmospheric pressure is (1.01 \times 10^{5}\text{ Pa}). Also give the excess pressure inside the drop.
- Q9.2(a): Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
- Q9.2(b): Explain why (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
- Q9.2(c): Explain why (c) Surface tension of a liquid is independent of the area of the surface
- Q9.2(d): Explain why (d) Water with detergent disolved in it should have small angles of contact.
- Q9.2(e): Explain why (e) A drop of liquid under no external forces is always spherical in shape
- Q9.20: What is the excess pressure inside a bubble of soap solution of radius (5.00\text{ mm}), given that the surface tension of soap solution at the temperature ((20^{\circ}\text{C})) is (2.50 \times 10^{-2}\text{ N m}^{-1}) ? If an air bubble of the same dimension were formed at depth of (40.0\text{ cm}) inside a container containing the soap solution (of relative density (1.20)), what would be the pressure inside the bubble ? (1 atmospheric pressure is (1.01 \times 10^{5}\text{ Pa})).
- Q9.3(a): Fill in the blanks using the word(s) from the list appended with each statement: (a) Surface tension of liquids generally . . . with temperatures (increases / decreases)
- Q9.3(b): Fill in the blanks using the word(s) from the list appended with each statement: (b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
- Q9.3(c): Fill in the blanks using the word(s) from the list appended with each statement: (c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . . . (shear strain / rate of shear strain)
- Q9.3(d): Fill in the blanks using the word(s) from the list appended with each statement: (d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)
- Q9.3(e): Fill in the blanks using the word(s) from the list appended with each statement: (e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)
- Q9.4(a): Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it
- Q9.4(b): Explain why (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
- Q9.4(c): Explain why (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
- Q9.4(d): Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
- Q9.4(e): Explain why (e) A spinning cricket ball in air does not follow a parabolic trajectory
- Q9.5: A (50\text{ kg}) girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter (1.0\text{ cm}). What is the pressure exerted by the heel on the horizontal floor ?
- Q9.6: Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density (984\text{ kg m}^{-3}). Determine the height of the wine column for normal atmospheric pressure.
- Q9.7: A vertical off-shore structure is built to withstand a maximum stress of (10^{9}\text{ Pa}). Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly (3\text{ km}), and ignore ocean currents.
- Q9.8: A hydraulic automobile lift is designed to lift cars with a maximum mass of (3000\text{ kg}). The area of cross-section of the piston carrying the load is (425\text{ cm}^{2}). What maximum pressure would the smaller piston have to bear ?
- Q9.9: A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with (10.0\text{ cm}) of water in one arm and (12.5\text{ cm}) of spirit in the other. What is the specific gravity of spirit ?
- Q10.1(a): Explain why (a) The blood pressure in humans is greater at the feet than at the brain
- Q10.1(b): Explain why (b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
- Q10.1(c): Explain why (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
- Q10.10: In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = 13.6)
- Q10.11: Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain.
- Q10.12: Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation ? Explain.
- Q10.13: Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is $4.0 \times 10^{-3} kg s^{-1}$, what is the pressure difference between the two ends of the tube ? (Density of glycerine = $1.3 \times 10^3 kg m^{-3}$ and viscosity of glycerine = $0.83 Pa s$). [You may also like to check if the assumption of laminar flow in the tube is correct].
- Q10.14: In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70 m s^{-1}$ and $63 m s^{-1}$ respectively. What is the lift on the wing if its area is $2.5 m^2$ ? Take the density of air to be $1.3 kg m^{-3}$.
- Q10.15: Figures 10.23(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- Q10.16: The cylindrical tube of a spray pump has a cross-section of $8.0 cm^2$ one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is $1.5 m min^{-1}$, what is the speed of ejection of the liquid through the holes ?
- Q10.17: A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5 \times 10^{-2} N$ (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?
- Q10.18: Figure 10.24 (a) shows a thin liquid film supporting a small weight = $4.5 \times 10^{-2} N$. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.
- Q10.19: What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of mercury at that temperature (20 °C) is $4.65 \times 10^{-1} N m^{-1}$. The atmospheric pressure is $1.01 \times 10^5 Pa$. Also give the excess pressure inside the drop.
- Q10.2(a): Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
- Q10.2(b): Explain why (b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
- Q10.2(c): Explain why (c) Surface tension of a liquid is independent of the area of the surface
- Q10.2(d): Explain why (d) Water with detergent disolved in it should have small angles of contact.
- Q10.2(e): Explain why (e) A drop of liquid under no external forces is always spherical in shape
- Q10.20: What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is $2.50 \times 10^{-2} N m^{-1}$ ? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble ? (1 atmospheric pressure is $1.01 \times 10^5 Pa$).
- Q10.3(a): Fill in the blanks using the word(s) from the list appended with each statement: (a) Surface tension of liquids generally . . . with temperatures (increases / decreases)
- Q10.3(b): Fill in the blanks using the word(s) from the list appended with each statement: (b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
- Q10.3(c): Fill in the blanks using the word(s) from the list appended with each statement: (c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . . . (shear strain / rate of shear strain)
- Q10.3(d): Fill in the blanks using the word(s) from the list appended with each statement: (d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)
- Q10.3(e): Fill in the blanks using the word(s) from the list appended with each statement: (e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)
- Q10.4(a): Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it
- Q10.4(b): Explain why (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
- Q10.4(c): Explain why (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
- Q10.4(e): Explain why (e) A spinning cricket ball in air does not follow a parabolic trajectory
- Q10.5: A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?
- Q10.6: Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 $kg m^{-3}$. Determine the height of the wine column for normal atmospheric pressure.
- Q10.7: A vertical off-shore structure is built to withstand a maximum stress of $10^9$ Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
- Q10.8: A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is $425 cm^2$. What maximum pressure would the smaller piston have to bear ?
- Q10.9: A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?
CBSE Solutions for Class 11 Physics Mechanical Properties of Fluids
Chapters in CBSE - Class 11 Physics
Top Tutors who teach Mechanical Properties of Fluids
Top Tutor
Zafarpur Mahawan, Karari
10 yrs of
Exp
1 student
287 hrs of classes completed
350
per hour
Online Classes
In my school, commerce is introduced in class 11th itself. So it became very significant that students are given all the basic information about their subjects and also to develop keen interest in them by relating the topics to their everyday life. With loads of practice and exemplary notes, the requisite foundation is made. And I make sure the topics are nicely delivered.
We took online mode from outside india, All classes held on time with excellent explanation and clear communication. Positive recommendations from my side.
Top Tutor
Mathara, Kozhikode
12 yrs of
Exp
3 students
921 hrs of classes completed
700
per hour
Online Classes
I can explain the concepts with clarity. I focus on solving numerical problems in Physics so that a student can learn better.
Top Tutor
Chembur West, Mumbai
17 yrs of
Exp
9 students
273 hrs of classes completed
750
per hour
Online Classes
Tutor's home
I am a teacher. I provide online and tutor home tuitions. I am M.Sc.(organic chemistry) B.Ed. I have an experience of teaching chemistry in Engineering college , schools (Aditya Birla Public School, Sagar public School),in coaching classes., home tuitions and online tuitions. I have around 15 years teaching experience.
My daughter took demo class on physics from Sheeba ma'am. She explained the topic in detail and helped in resolving the doubts. Overall a helpful session.
Super Tutor
Patpar Ganj, Delhi
20 yrs of
Exp
10 students
971 hrs of classes completed
500
per hour
Online Classes
Student's Home
I am a teacher. I love teaching and want to share my knowledge with my students. I will take online classes. My approach combines clear concepts, regular practice, and student-friendly strategies to make learning effective and enjoyable.
My tutor is very thorough and took careful measures in helping me grasp a concept that I had forgotten." "he made me really think about how I would come up with the answer." "I liked how he is straight forward and to the point." "Great tutor that helped me so much!"
Super Tutor
KK Nagar Sector 10, Chennai
20 yrs of
Exp
10 students
2097 hrs of classes completed
600
per hour
Online Classes
Student's Home
Tutor's home
I will make mathematics is for students. Since 11th std is so important for students. It has basic concepts. I will make everything will be easy for students
This tutor is exceptional at teaching; they explain complex concepts clearly, resolve all doubts, and provide step-by-step solutions to every question.
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Physics Mechanical Properties of Fluids EXERCISES worksheets
Download Now
