Question

A Venturi tube may be used as a fluid flow meter. If the fluid flow rate in m³/s is 1.6 * 10^-3 and the radius R₁ = 2.4 *10^-2 m of the inlet tube is 2.9 times the radius R₂ of the outlet tube, and the fluid is water (ρ = 1000 kg/m³), find the pressure difference P₁ - P₂ in units of kPa.

Enter a number with one digit behind the decimal point.

Answer 1

let v1 is the speed at R1

volume flow rate, dV/dt = A1*v1

dV/dt = pi*R1^2*v1

==> v1 = (dV/dt)/(pi*R1^2)

= 1.6*10^-3/(pi*0.024^2)

= 0.884 m/s

now use continuty equation,

A2*v2 = A1*v1

pi*R2^2*v2 = pi*R1^2*v1

v2 = (R1/R2)^2*v1

= (2.9*R2/R2)^2*0.884

= 7.43 m/s

now use Pascal's law

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

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

= (1/2)*1000*(7.43^2 - 0.884^2)

= 27212 Pa

= 27.2 kPa <<<<<<----------------Answer