For the pipe enlargement shown in the figure below the press

For the pipe enlargement shown in the figure below, the pressures at sections (1) and (2) are 60 and 64 psi, respectively. Determine the weight flowrate (lb/s) of the gasoline in the pipe.

Solution

Q= rho x A₁ x V₁ = rho x A₂ x V₂ but rho can be assumed to be constant since there is no temperature chnage is given.

there fore V₂ = (A₁ x V₁)/A₂

A₁ = 3.14 x 2.05²/4. = 3.38 sq. in

A₂ = 3.14 x 3.71 ² /4 = 10.80 sq in.

according to Bernaulis equation, since the tube is horizontal,

P₁ + 0.5 V₁² = P₂ + 0.5 x V₂²

60 + 0.5 V₁² = 64 + 0.5 {( A₁x V₁) / A₂}²

0.5 V1² - 0.5 {( 3.38/10.8) x V1}² = 64-60 = 4 psi

V₁² - ( 0.3129 V₁)² = 8 psi

V₁^2-.097V₁² = 8 psi

V₁ = sqrt ( 8/ 0.902) = 2.98 in/sec

there fore the flow Q = A1 x V1 = 3.38 x 2.98 = 10.06 in³ /sec