Question

An ideal fluid flows through a pipe of a circular cross section made of two sections with diameter 2.5 cm and 3.5 cm calculate the ratio of a velocity v​

Answer 1

Let two cross section of the Pipe be A and B.

For Cross-section A,

∴ Diameter of cross section A = 2.5 cm.

Radius of Cross section A = 2.5/2 cm.

For Cross-section B,

∴ Diameter of cross section B = 3.5 cm.

Radius of Cross section B = 3.5/2 cm.

Using the Equation of Continuity,

     $a_AV_A = a_BV_B$

∴ $\frac{V_A}{V_B} = \frac{a_B}{a_A}$

$\frac{V_A}{V_B} = \frac{3.5^{2} }{2.5^{2}}$

$\frac{V_A}{V_B} = \frac{49}{25}$

Hence, the ratio of the velocity of the fluid in pipe A to Pipe B is 49 : 25.

Hope it helps.

Answer 2

For Cross-section A,

∴ Diameter of cross section A = 2.5 cm.

Radius of Cross section A = 2.5/2 cm.

For Cross-section B,

∴ Diameter of cross section B = 3.5 cm.

Radius of Cross section B = 3.5/2 cm.