Question

The area of cross-section of water stream coming out of tape at depth $h_0$ below tap in terms of 'a' just after the opening of the tap.

• A. $\frac{a}{\sqrt{1.98}}$
• B. $\frac{a}{\sqrt{.98}}$
• C. $\frac{2a}{\sqrt{1.98}}$
• D. $\frac{a}{\sqrt{1.38}}$

Answer 1

The correct option is A $\frac{a}{\sqrt{1.98}}$

Applying Bernoulli's equation between (2) and (3)
$\frac{1}{2}p{v}_2^2+pg{h}_0=\frac{1}{2}p{v}_3^2$
Through continuity equation -
$a{v}_2=a^{\prime }{v}_3\Rightarrow v_3=\frac{a{v}_2}{a^{\prime }}$
$\Rightarrow$$\frac{1}{2}p{v}_2^2+pg{h}_0=\frac{1}{2}p{\left(\frac{a{v}_2}{a^{\prime }}\right)}^2$
$\frac{1}{2}\times 2\times 2+g{h}_0=\frac{1}{2}{\left(\frac{a}{a^{\prime }}\right)}^2\times 2\times 2$
${\left(\frac{a}{a^{\prime }}\right)}^2=1+\frac{9.8\times 20}{2}\Rightarrow {\left(\frac{a}{a^{\prime }}\right)}^2=1.98\Rightarrow a^{\prime }=\frac{a}{\sqrt{1.98}}$