An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is

Question

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is (A) 9: 4 (B) 3: 2 (C) √3: √2 (D) √2: √3

Tardigrade Admin · Accepted Answer

As, A1v1=A2v2 ⇒ (v1/v2)=(A2/A1)=((π D22/4)/(π D21/4)) =((D2/D1))2 or (v1/v2)=((3.75 cm/2.5 cm))2 =2.25=9:4

Q. An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters $2.5 c m$ and $3.75 c m$ . The ratio of the velocities in the two pipes is

$9 : 4$

$3 : 2$

$3 : 2$

$2 : 3$

As,
$A_{1} v_{1} = A_{2} v_{2}$
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{A _{2}}{A _{1}} = \frac{( π D _{2}^{2} /4 )}{( π D _{1}^{2} /4 )}$
$= (\frac{D _{2}}{D _{1}})^{2}$
or $\frac{v _{1}}{v _{2}} = (\frac{3.75 c m}{2.5 c m})^{2}$
$= 2.25 = 9 : 4$

Q. An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters 2.5cm and 3.75cm. The ratio of the velocities in the two pipes is

9:4

3:2

3​:2​

2​:3​

As, A1​v1​=A2​v2​ ⇒v2​v1​​=A1​A2​​=(πD12​/4)(πD22​/4)​ =(D1​D2​​)2 or v2​v1​​=(2.5cm3.75cm​)2 =2.25=9:4

Q. An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters $2.5 c m$ and $3.75 c m$ . The ratio of the velocities in the two pipes is

$9 : 4$

$3 : 2$

$3 : 2$

$2 : 3$

As,
$A_{1} v_{1} = A_{2} v_{2}$
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{A _{2}}{A _{1}} = \frac{( π D _{2}^{2} /4 )}{( π D _{1}^{2} /4 )}$
$= (\frac{D _{2}}{D _{1}})^{2}$
or $\frac{v _{1}}{v _{2}} = (\frac{3.75 c m}{2.5 c m})^{2}$
$= 2.25 = 9 : 4$