Find the best tutors and institutes for Class 11 Tuition
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)
Solution :
Step 1: Theoretical Foundation of Reynolds Number
The transition from laminar flow to turbulent flow in a fluid is governed by the dimensionless quantity known as the Reynolds number ($Re$), defined by the expression:
$Re = \frac{\rho v D}{\eta}$
Where:
- $\rho$ = Density of the fluid [kg/m³]
- $v$ = Flow velocity of the fluid [m/s]
- $D$ = Characteristic linear dimension (characteristic length of the object) [m]
- $\eta$ = Dynamic viscosity of the fluid [Pa·s]
[Per the principle of dynamic similarity in fluid mechanics, the flow regime transition occurs at a specific critical Reynolds number ($Re_c$).]
Step 2: Comparison of Model and Actual Plane
For both the scale model in the wind tunnel and the actual plane in flight, the fluid medium (air) remains the same, implying $\rho$ and $\eta$ are constant across both scenarios. To maintain dynamic similarity (i.e., to have the same $Re$ for the model and the actual plane), the following relationship must hold:
$v_m D_m = v_a D_a$
Where subscript '$m$' denotes the model and '$a$' denotes the actual plane.
Step 3: Analytical Derivation of Velocity
Rearranging the equation to solve for the velocity $v$:
$v = \frac{Re_c \cdot \eta}{\rho \cdot D}$
From this equation, it is evident that velocity $v$ is inversely proportional to the characteristic dimension $D$ ($v \propto \frac{1}{D}$).
Since the scale model of a plane is significantly smaller than the actual plane ($D_m \ll D_a$), it mathematically follows that the velocity required to reach the critical Reynolds number for the model must be significantly higher than the velocity required for the actual plane.
Step 4: Visualizing Fluid Flow Regimes
Step 5: Final Logical Deduction
Because the dimension $D$ for the model is smaller, the denominator in the proportionality $v \propto \frac{1}{D}$ decreases, forcing $v$ to increase to maintain the same critical $Re$ at which turbulence initiates. Therefore, the model reaches turbulence at a greater speed compared to the speed at which the actual plane would transition to turbulence under identical fluid conditions.
Final Solution: For the model of a plane in a wind tunnel, turbulence occurs at a greater speed for turbulence for an actual plane.
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)
- Q10.4(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(d): Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
- 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
HMT Estate 2nd Stage, Bangalore
20 yrs of
Exp
32 students
2767 hrs of classes completed
550
per hour
Online Classes
I am a teacher. Teaching chemistry for the past 20+ years. I also have some experience in research in applied chemistry. I have a masters degree in chemistry and a bachelors degree in education. In addition to teaching I have experience in school administration and content development. My key skills are to train the students for various competitive exams like JEE, NEET, BITSAT, CET.
She is patient , understanding and then times the classes as per the students requirements. Gentle and slow. The right kind of teacher for chemistry subject.
Top Tutor
Mukherjee Nagar, Delhi
5 yrs of
Exp
2057 hrs of classes completed
500
per hour
Online Classes
Hi, I am Neeraj Dwivedi Top Tutor and partner at Urban Pro . Into profession of teaching since last four years. Expertise and specialization in guiding students on subjects like History, Political Science, Economics and Hindi. These subjects were my strength in my journey of Civil Services and later helped in shaping future of students. Apart from teaching guidance I have been doing career counselling of students as to what to pursue/not pursue after school based on individual interests and capabilities.
I scored above in all three subjects and you are good in explaining the details, I really amazed by your teaching style.
Top Tutor
Sarv Suvidha Nagar, Indore
1 yrs of
Exp
3 students
200 hrs of classes completed
200
per hour
Online Classes
"I am an AI-enabled Social Science educator with experience teaching at Physics Wallah. I specialize in making complex concepts simple through storytelling and visual learning. I am passionate about creating engaging and effective learning experiences for students. I would love to contribute my skills as a tutor on your platform."
Teaches with great efforts, always ready to explain concepts acc to the needs and requirements of student and also comes up with different teaching styles for giving concept clarity...
Top Tutor
Naskar Bagan, Kolkata
2 yrs of
Exp
5 students
209 hrs of classes completed
400
per hour
Online Classes
Student's Home
Tutor's home
🚀 High-Impact Computer Science & IP Tutoring for CBSE& CISCE Class 10, 11 & 12 Hi! I’m a B.C.A. graduate and experienced online educator dedicated to helping students build genuine logical thinking and ace their board examinations. Having scored 94/100 in my own Class 12 Computer Science boards using highly efficient study strategies, I know exactly how to simplify the syllabus for maximum understanding and top marks. I bridge the gap between memorizing syntax and actually understanding how to code. 🌟 Why Choose My Classes? 1. Targeted Expertise: Specialized coaching for CBSE & CISCE Class 10 ,11 & 12 Computer Science, Informatics Practices (IP), and Information Technology (including Java, Python programming and database management). 2. Proven Resources: Standard reference alignment, custom study notes, topic-wise assignments, and rigorous mock tests. 3. Interactive Learning: 100% online sessions utilizing dynamic PPTs and live whiteboards—no boring lectures, just hands-on, practical coding. 4. Track Record: Successfully coached students from top schools to become confident, independent problem solvers. 5. My Approach: I don't just teach you how to write code; I teach you how to think like a programmer so you can approach any exam question with confidence. Let’s turn coding anxiety into board exam success.
He is the best teacher. He explains in easy language and develops a good bond with the student.
Top Tutor
Sector 5, Gurgaon
14 yrs of
Exp
5 students
2607 hrs of classes completed
500
per hour
Online Classes
Tutor's home
I have substantial experience providing tuition to Class 11 students in Mathematics, focusing on helping them master the subject and prepare for their academic and competitive exams. My approach includes: 1. In-Depth Curriculum Understanding: Core Topics: I cover all major topics in the Class 11 Maths curriculum, including algebra, calculus, trigonometry, coordinate geometry, and statistics. Advanced Concepts: I delve into more advanced concepts, ensuring students have a strong foundation for Class 12 and beyond. 2. Personalized Teaching Methods: Customized Lessons: I tailor my lessons to meet the individual needs of each student, addressing their specific strengths and weaknesses. Interactive Sessions: I use interactive teaching methods, including problem-solving sessions, real-world applications, and group discussions, to make learning engaging and effective. 3. Exam Preparation: School Exams: I help students prepare for their school exams by providing thorough revision sessions, practice tests, and previous years' question papers. Competitive Exams: I also prepare students for competitive exams like the JEE, focusing on building their problem-solving skills and time management. 4. Use of Technology and Resources: Educational Tools: I incorporate technology, using online tools and educational software to enhance the learning experience. Multimedia Resources: I use visual aids, interactive simulations, and other multimedia resources to explain complex concepts more clearly. 5. Continuous Assessment and Feedback: Regular Tests: I conduct regular tests and quizzes to assess students' understanding and track their progress. Feedback and Improvement: I provide detailed feedback and work with students on areas that need improvement, ensuring continuous growth. 6. Mentoring and Support: Academic Guidance: I offer guidance on academic goals, study strategies, and time management to help students achieve their full potential. Emotional Support: I provide a supportive learning environment, encouraging students to ask questions, express their concerns, and build confidence in their abilities. My detailed and personalized approach to teaching Class 11 Mathematics has helped many students excel in their studies and build a strong foundation for their future academic and professional pursuits.
Rinku sir is very friendly and makes learning maths fun and enjoyable. His way of teaching is excellent and he explains concepts clearly and patiently. With Sir's guidance, I was able to cover more topics in less time while developing a better understanding of the concepts. Highly recommended!
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Physics Mechanical Properties of Fluids EXERCISES worksheets
Download Now
