A Venturi meter is a device used for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed $ v_2 $ through a horizontal section of pipe with a cross-sectional area $ A_2 = 542\,\text{cm}^2 $. The gas has a density of $ 1.35\,\text{kg/m}^3 $. The Venturi meter has a cross-sectional area of $ A_1 = 215\,\text{cm}^2 $ and has been substituted for a section of the larger pipe. The pressure difference between the two sections $ P_2 – P_1 = 145\,\text{Pa} $.

Question

A Venturi meter is a device used for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed $ v_2 $ through a horizontal section of pipe with a cross-sectional area $ A_2 = 542\,\text{cm}^2 $. The gas has a density of $ 1.35\,\text{kg/m}^3 $. The Venturi meter has a cross-sectional area of $ A_1 = 215\,\text{cm}^2 $ and has been substituted for a section of the larger pipe. The pressure difference between the two sections $ P_2 &#8211; P_1 = 145\,\text{Pa} $.(a) Find the speed $ v_2 $ of the gas in the larger original pipe.
, (b) Find the speed $ v_1 $ of the gas in the Venturi meter.
, (c) What is the volume flow rate $ Q $ of the gas (in $ \text{m}^3/\text{sec} $)?
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Jason · Accepted Answer

$\boxed{v_2 \approx 6.33\ \text{m/s}}$
$\boxed{v_1 \approx 16.0\ \text{m/s}}$
$\boxed{Q \approx 0.343\ \text{m}^3/\text{s}}$

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