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Mechanical Properties of Fluids — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMechanical Properties of Fluids3 Marks
Question
A liquid is flowing through a horizontal pipe of varying cross section. At a certain point, where the diameter of the pipe is $5 \mathrm{~cm}$, the flow velocity is $0.25 \mathrm{~m} / \mathrm{s}$. What is the flow velocity where the diameter is $1 \mathrm{~cm}$ ?
✓

Answer


Data : $d_1=5 \mathrm{~cm}, v_1=0.25 \mathrm{~m} / \mathrm{s}, \mathrm{d}_2=1 \mathrm{~cm}$ According to the equation of continuity of flow, $A_1 \rho_1 v_1=A_2 \rho_2 v_2$
where $A_1$ and $p_1$ are the cross-sectional area and density of the liquid where the flow velocity is $v_1 ; A_2$ and $\rho_2$ are the corresponding quantities where the flow velocity is $v_2$.
Assuming the liquid is incompressible,
$
\begin{aligned}
\rho_1 & =\rho_2 \\
\therefore A_1 v_1 & =A_2 v_2 \\
\therefore v_2 & =\frac{A_1}{A_2} \nabla_1 \quad \\
& =\frac{\left(\pi d_1^2 / 4\right)}{\left(\pi d_2^2 / 4\right)} \nabla_1=\left(\frac{d_1}{d_2}\right)^2 \nabla_1 \\
& =\left(\frac{5 \mathrm{~cm}}{1 \mathrm{~cm}}\right)^2(0.25 \mathrm{~m} / \mathrm{s}) \\
& =25 \times 0.25=6.25 \mathrm{~m} / \mathrm{s}
\end{aligned}
$

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