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A venturimeter has a pipe diameter of $4 \mathrm{~cm}$ and a throat diameter of $2 \mathrm{~cm}$. Velocity of water in the pipe section is $10 \mathrm{~m} / \mathrm{s}$. The pressure drop, between pipe section and the throat section is
[use density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]
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[use density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]
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1925 Upvotes
Verified Answer
The correct answer is:
$7.5 \times 10^5 \mathrm{~Pa}$
By equation of continuity
$$
\begin{aligned}
& A_1 V_1=A_2 V_2 \\
& \pi(4)^2 \times 10=\pi(2)^2 \times V \\
& V=40 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
Also, By Bernoulli's theorem
$$
\begin{aligned}
& \mathrm{P}_1+\frac{1}{2} \rho \mathrm{V}_1^2=\mathrm{P}_2+\frac{1}{2} \rho \mathrm{V}_2^2 \Rightarrow \mathrm{P}_1-\mathrm{P}_2=\frac{1}{2} \rho\left(\mathrm{V}_2^2-\mathrm{V}_1^2\right) \\
& =\frac{1}{2} \times 1000 \times 1500=7.5 \times 10^5 \mathrm{~Pa}
\end{aligned}
$$
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