Question

Water is flowing continuously from a tap having a bore of internal diameter
8 $\times$ ${10}^{-3}$ m. Calculate the diameter of the water stream at a distance 2 $\times$ ${10}^{-1}$ m below the tap. Assume that water velocity as it leaves the tap is 4 $\times$ ${10}^{-1}$ m/s

• A. 3.54 10^-3 m
• B. 3.54 10^-1 m.
• C. 3.54 10^-2 m
• D. 3.54 10^-4 m.

Answer 1

The correct option is A

3.54 10^-3 m

$\Rightarrow$ $v_2^2=v_1^2+2gh$ ..... (i)

From continuity equation , $A_1{v}_1=A_2{v}_2$

$\Rightarrow$ $\pi r_1^2{v}_1=\pi r_2^2{v}_2$ $\Rightarrow$ $r_2=r_1{\left(\frac{v_1}{v_2}\right)}^{\frac{1}{2}}$

$\therefore$ $d_2=d_1{\left(\frac{V_1}{V_2}\right)}^{\frac{1}{2}}$ ............ ( ii)

From (i) & (ii),

$d_2=d_1{\left[\frac{v_1}{(v_1^2+2gh{)}^{\frac{1}{2}}}\right]}^{\frac{1}{2}}$ ≈ 3.54 × ${10}^{-3}$ m.