ch 12 Fuids Item 4 Item 4 A pair of vertical, open-ended glass tubes inserted in

Question

ch 12 Fuids Item 4 Item 4 A pair of vertical, open-ended glass tubes inserted into a horizontal pipe are often used together to measure flow velocity in the pipe, a configuration called a Venturi meter. Consider such an arrangement with a horizontal pipe carrying fluid of density p. The fluid rises to heights hi and h2 in the two open-ended tubes (see figure). The cross- sectional area of the pipe is Ai at the position of tube 1, and A2 at the position of tube 2. Figure Figure 1 rofl Tube I Tube 2

Explanation / Answer

A)
Pressure below tube 1, P1 = Po + rho*g*h1

P1 - Po = rho*g*h1

P1_gauge = rho*g*h1 <<<<<<<<------------------Answer

B)

Pressure below tube 2, P2 = Po + rho*g*h2

A1*v1 = A1*v2

v2 = A1*v1/A2

use Bernoullie's theorem,

P1 + (1/2)*rho*v1^2 = P2 + (1/2)*rho*v2^2

Po + rho*g*h1 + (1/2)*rho*v1^2 = Po + rho*g*h2 + (1/2)*rho*v2^2

rho*g*(h1-h2) = (1/2)*rho*(v2^2 - v1^2)

g*(h1-h2) = (1/2)*((A1*v1/A2)^2 - v1^2)

2*g*(h1-h2) = ( (A1/A2)^2 - 1)*v1^2

==> v1 = sqrt(2*g*h/( (A1/A2)^2 - 1) )

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