Question:
A pipe has cross-sectional areas $4$ cm$^2$ and $1$ cm$^2$. If velocity in the wider section is $2$ m/s, velocity in the narrower section is:
A pipe has cross-sectional areas $4$ cm$^2$ and $1$ cm$^2$. If velocity in the wider section is $2$ m/s, velocity in the narrower section is:
Show Hint
The velocity of a fluid is inversely proportional to the cross-sectional area ($v \propto 1/A$). If the area decreases by a factor of 4 (from 4 to 1), the velocity must increase by a factor of 4 ($2 \times 4 = 8$).
Updated On: May 20, 2026
- $2$ m/s
- $4$ m/s
- $8$ m/s
- $16$ m/s
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
For an incompressible fluid flowing through a pipe of varying cross-section, the principle of continuity applies. It states that the mass flow rate remains constant throughout the pipe, which leads to the equation:
\[ A_1 v_1 = A_2 v_2 \]
Where:
• $A$ is the cross-sectional area.
• $v$ is the velocity of the fluid at that section.
Step 1: Identify the given values.
From the provided problem data:
• Area of wider section ($A_1$) = $4$ cm$^2$
• Velocity in wider section ($v_1$) = $2$ m/s
• Area of narrower section ($A_2$) = $1$ cm$^2$
Step 2: Apply the Equation of Continuity.
Substitute the known values into the formula: \[ (4 \text{ cm}^2) \times (2 \text{ m/s}) = (1 \text{ cm}^2) \times v_2 \] \[ 8 \text{ cm}^2 \cdot \text{m/s} = 1 \text{ cm}^2 \cdot v_2 \]
Step 3: Solve for the unknown velocity.
\[ v_2 = \frac{8}{1} \text{ m/s} \] \[ v_2 = 8 \text{ m/s} \]
• $A$ is the cross-sectional area.
• $v$ is the velocity of the fluid at that section.
Step 1: Identify the given values.
From the provided problem data:
• Area of wider section ($A_1$) = $4$ cm$^2$
• Velocity in wider section ($v_1$) = $2$ m/s
• Area of narrower section ($A_2$) = $1$ cm$^2$
Step 2: Apply the Equation of Continuity.
Substitute the known values into the formula: \[ (4 \text{ cm}^2) \times (2 \text{ m/s}) = (1 \text{ cm}^2) \times v_2 \] \[ 8 \text{ cm}^2 \cdot \text{m/s} = 1 \text{ cm}^2 \cdot v_2 \]
Step 3: Solve for the unknown velocity.
\[ v_2 = \frac{8}{1} \text{ m/s} \] \[ v_2 = 8 \text{ m/s} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Fluid Dynamics Questions
- A fluid flows through a pipe of diameter 5 cm with a velocity 2 m/s. If the pipe is constricted to a diameter of 3 cm, the velocity of fluid at the constriction is:
- A large open top water tank is completely filled with water. A small hole of diameter 4 mm is made 10 m below the water level. The flow rate of water through the hole is:
- A steel ball of radius 0.05 cm and density \( 7.8 \, \text{g/cm}^3 \) is dropped into water. What is its terminal velocity?
(Density of water \( = 1 \, \text{g/cm}^3 \), Viscosity of water \( = 0.001 \, \text{Pas} \)) - If two rain drops of radii $r_1$ and $r_2$ reach the ground with terminal velocities $v_1$ and $v_2$ and linear momenta $p$ and $32p$ respectively, then $r_1 : r_2 =$
- Water flows in a horizontal pipe. At a point where speed is $2$ m/s, pressure is $2000$ Pa. At another point, speed becomes $4$ m/s. Find pressure at second point. (Density $= 1000$ kg/m$^3$)
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions