Answered: The Venturi meter shown in the sketch…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

The Venturi meter shown in the sketch below, contracts the flow down to one quarter of its original area. Cold air at 0 deg C flows in the pipe through the Venturi meter. The velocity of the air upstream of the Venturi meter is equal to 40 ft/s and the pressure at the same point is equal to 30 psia. What is the manometer reading if the fluid of the manometer is water with density 1000 kg/m³. Assume that the air behaves as an ideal gas with molecular weight equal to Mw=29 kg/kmol and constant density evaluated at upstream conditions. Use Bernoulli's equation for your calculations.

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Answer

From Bernoulli's equation we have

$\frac{P_{1}}{γ_{a}} + \frac{{v_{1}}^{2}}{2 g} + z_{1} = \frac{P_{2}}{γ_{a}} + \frac{{v_{2}}^{2}}{2 g} + z_{2} + h_{L}$

$\frac{P_{1}}{γ_{a}} - \frac{P_{2}}{γ_{a}} + z_{1} = \frac{{v_{2}}^{2}}{2 g} - \frac{{v_{1}}^{2}}{2 g} + z_{2} + h_{L}$

P₁ and P₂ are pressure at upstream and contracted section respectively

v₁ and v₂ are velocity at upstream and contracted section respectively

z₁ and z₂ are elevation head, since venturimeter will be at same level z₁ = z₂ =0

h_L = major and minor headloss

h_L =0

$\frac{P_{1} - P_{2}}{γ_{a}} = \frac{{v_{2}}^{2} - {v_{1}}^{2}}{2 g}$

$\frac{P_{1} - P_{2}}{γ_{a}} = \frac{(γ_{w} - γ_{a}) h}{γ_{a}} = (\frac{γ_{w}}{γ_{a}} - 1) h$

$(\frac{γ_{w}}{γ_{a}} - 1) h = \frac{{v_{2}}^{2} - {v_{1}}^{2}}{2 g}$ ..say equation I

$γ_{w}$ = unit weight of water

$γ_{w}$ = 62.4 lb/ft³

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