Physics Tutor in Thane Mumbai – Concept Clarity with Kumar Sir
+91-9958461445
If you live in Thane Mumbai and Physics is not becoming clear, then the problem is usually not intelligence; the problem is weak concept clarity. Many students attend school, coaching and online lectures, but still they get stuck when numerical questions come. This happens especially in NEET Physics, IIT JEE Physics, CBSE Physics, ICSE Physics, IB Physics, IGCSE Physics, A-Level Physics and AP Physics.
At Kumar Physics Classes, Kumar Sir teaches Physics from the basic level to the advanced level. He explains every concept with diagrams, derivations, logic and numerical application. For students living in Thane, Hiranandani Estate, Manpada, Ghodbunder Road, Naupada, Panch Pakhadi, Vasant Vihar, Majiwada, Kolshet Road and nearby areas, Kumar Sir provides focused Physics guidance for school exams, NEET and IIT JEE.
Continuity Equation in Bernoulli’s Theorem
In fluid mechanics, the equation of continuity is based on conservation of mass. If an incompressible liquid flows through a pipe of different cross-sectional areas, then the volume of liquid crossing every section per second remains constant.
Equation of Continuity:
A₁v₁ = A₂v₂
Here, A₁ and A₂ are cross-sectional areas, and v₁ and v₂ are velocities of liquid at those sections.
This means when area decreases, velocity increases. This concept is very important before understanding Bernoulli’s theorem, because Bernoulli’s theorem connects pressure, velocity and height of a flowing liquid.
Conceptual Question on Continuity Equation
Question:
Water flows through a horizontal pipe. At one point, the area of cross-section is 4 cm² and velocity is 2 m/s. At another point, the area becomes 1 cm². Find the velocity of water at the narrow part.
Solution:
Using equation of continuity:
A₁v₁ = A₂v₂
4 × 2 = 1 × v₂
v₂ = 8 m/s
So, velocity of water at the narrow part is 8 m/s.
Kumar Sir’s Contact Details
Kumar Physics Classes
Phone: +91-9958461445
Email: kumarsirphysics@gmail.com
Website: https://kumarphysicsclasses.com
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Equation of Continuity – 50 Conceptual Questions With Answers
Kumar Physics Classes | +91-9958461445 | www.kumarphysicsclasses.com
Equation of Continuity is based on conservation of mass. For incompressible liquid:
- Question: What is the principle behind equation of continuity?
Answer: Conservation of mass. - Question: Write equation of continuity for incompressible liquid.
Answer: A₁v₁ = A₂v₂. - Question: If area decreases, what happens to velocity?
Answer: Velocity increases. - Question: If area increases, what happens to velocity?
Answer: Velocity decreases. - Question: Is continuity equation valid for compressible fluids in simple form?
Answer: No, for compressible fluids density must be included. - Question: General continuity equation is?
Answer: ρ₁A₁v₁ = ρ₂A₂v₂. - Question: For incompressible fluid, why does density cancel?
Answer: Because density remains constant. - Question: Water flows from wider pipe to narrower pipe. Where is speed more?
Answer: In the narrower pipe. - Question: If A₁ = 4 cm², v₁ = 2 m/s, A₂ = 2 cm², find v₂.
Answer: v₂ = 4 m/s. - Question: If area becomes one-fourth, velocity becomes?
Answer: Four times. - Question: If velocity becomes double, area becomes?
Answer: Half. - Question: Does continuity equation depend on pressure?
Answer: No, it depends on mass flow rate. - Question: What remains constant in steady incompressible flow?
Answer: Volume flow rate Av. - Question: Unit of volume flow rate is?
Answer: m³/s. - Question: Unit of mass flow rate is?
Answer: kg/s. - Question: Why does water jet become thinner while falling?
Answer: Speed increases due to gravity, so area decreases. - Question: In a pipe, A₁ = 10 cm², v₁ = 3 m/s, A₂ = 5 cm². Find v₂.
Answer: v₂ = 6 m/s. - Question: If radius of pipe becomes half, area becomes?
Answer: One-fourth. - Question: If radius becomes half, velocity becomes?
Answer: Four times. - Question: If radius doubles, velocity becomes?
Answer: One-fourth. - Question: Why is speed high at narrow nozzle?
Answer: Because area is small, so velocity increases to maintain Av constant. - Question: Does continuity equation apply to turbulent flow simply?
Answer: It applies to mass conservation, but simple formula is best for steady streamline flow. - Question: What is steady flow?
Answer: Flow in which fluid properties at a point do not change with time. - Question: Is equation of continuity scalar or vector relation?
Answer: It is mainly a scalar relation for flow rate. - Question: In A₁v₁ = A₂v₂, what is A?
Answer: Cross-sectional area. - Question: In A₁v₁ = A₂v₂, what is v?
Answer: Speed of fluid. - Question: If A₂ is smaller than A₁, compare v₂ and v₁.
Answer: v₂ is greater than v₁. - Question: If A₂ = A₁/5, then v₂ = ?
Answer: v₂ = 5v₁. - Question: If v₂ = 3v₁, then A₂ = ?
Answer: A₂ = A₁/3. - Question: Is continuity equation used in Bernoulli’s theorem?
Answer: Yes, it helps relate area and velocity. - Question: What happens to pressure at narrow part in horizontal pipe?
Answer: Pressure decreases as velocity increases. - Question: Which theorem explains pressure change with velocity?
Answer: Bernoulli’s theorem. - Question: Continuity equation alone tells about pressure or velocity?
Answer: Velocity relation with area. - Question: A pipe has area 6 cm² and speed 4 m/s. Area becomes 3 cm². Speed?
Answer: 8 m/s. - Question: A pipe has radius r and speed v. Radius becomes 2r. Speed?
Answer: v/4. - Question: A pipe has radius r and speed v. Radius becomes r/3. Speed?
Answer: 9v. - Question: Why does a garden hose spray faster when mouth is pressed?
Answer: Area decreases, so velocity increases. - Question: What is discharge?
Answer: Volume of liquid flowing per second. - Question: Formula of discharge?
Answer: Q = Av. - Question: Is discharge constant in steady incompressible flow?
Answer: Yes. - Question: If Q = 20 cm³/s and A = 5 cm², find v.
Answer: v = 4 cm/s. - Question: If Q = 12 m³/s and v = 3 m/s, find A.
Answer: A = 4 m². - Question: Can liquid accumulate inside a pipe in steady flow?
Answer: No, mass entering equals mass leaving. - Question: Why is continuity equation important in NEET Physics?
Answer: It is used in fluid mechanics numericals and Bernoulli applications. - Question: Why is continuity equation important in JEE Physics?
Answer: It helps solve advanced fluid flow problems involving area, speed and pressure. - Question: If two pipes carry same discharge, which pipe has higher speed?
Answer: The pipe with smaller area. - Question: If speed is high, area must be?
Answer: Small, for same discharge. - Question: If speed is low, area must be?
Answer: Large, for same discharge. - Question: What is the most common mistake in continuity equation?
Answer: Students forget that area depends on radius squared. - Question: Final concept: why does A₁v₁ = A₂v₂?
Answer: Because in steady incompressible flow, the same volume of liquid must pass through every cross-section per second.
Kumar Physics Classes
Phone: +91-9958461445
Website: www.kumarphysicsclasses.com
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