Question
Why does velocity increase when water flowing in broader pipe enters a narrow pipe?
✓
Answer
When a tube narrows, the same volume occupies a greater length, as schematically shown in below figure.
$A_1$ is the cross section of the broader pipe and that of narrower pipe is $A_2$.
By the equation of continuity, $V_2 = (A_1/A_2)V_1$
Since $A_1/A_2 > v_2 > v_1$. For the same volume to pass points $1$ and $2$ in a given time, the speed must be greater at point $2$.
The process is exactly reversible. If the fluid flows in the opposite direction, its speed decreases when the tube widens.
$A_1$ is the cross section of the broader pipe and that of narrower pipe is $A_2$.
By the equation of continuity, $V_2 = (A_1/A_2)V_1$
Since $A_1/A_2 > v_2 > v_1$. For the same volume to pass points $1$ and $2$ in a given time, the speed must be greater at point $2$.
The process is exactly reversible. If the fluid flows in the opposite direction, its speed decreases when the tube widens.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The lower end of a capillary tube of diameter $1 \mathrm{~mm}$ is dipped $10 \mathrm{~cm}$ below the water surface in a beaker. What pressure is required to blow a hemispherical air bubble at the lower end of the tube? Present your answer rounded off to 4 significant figures. [Surface tension $=0.072$ $\mathrm{N} / \mathrm{m}$, density $=10^3 \mathrm{~kg} / \mathrm{m}^3$, atmospheric pressure $\left.=101.3 \mathrm{kPa}, \mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right]$
→State the uses of a potentiometer.
What is an electromagnet?
Distinguish between forced vibrations and resonance. Draw neat, labelled diagrams for the modes of vibration of a stretched string in second harmonic and third harmonic.
Discuss the necessity of radius of gyration. Define it. On what factors does it depend and it does not depend? Can you locate some similarity between the centre of mass and radius of gyration? What can you infer if a uniform ring and a uniform disc have the same radius of gyration?
Explain why the magnetic force on a charged particle cannot change the linear speed and the kinetic energy of the particle.###One implication of the Lorentz force law is that magnetic force does no work. Justify.
Find the capacity of a capacitor which when put in series with a $10 \Omega$ resistor makes the power factor equal to $0.5.$ Assume an $80\ V-100\ Hz\ AC$ supply.
→State the postulates of Bohr’s atomic model. Hence show the energy of electrons varies inversely to the square of the principal quantum number.
The angular position of a rotating object is given by $\theta(t)=\left(1.55 t^2-7.75 t+2.87\right)$ rad, where $t$ is measured in second.
(i) When is the object momentarily at rest?
(ii) What is the magnitude of its angular acceleration at that time?
→(i) When is the object momentarily at rest?
(ii) What is the magnitude of its angular acceleration at that time?
Obtain an expression for the electric potential at a point due to an isolated point charge.