Question

A horizontal pipe carries a smoothly flowing liquid of density of 1110 kg/m3. At Locations 1 and 2 along the pipe, the diameters are d₁=5.45 cm and d₂=2.83 cm, respectively. The flow speed at Location 1 is 2.83 m/s. What is the pressure difference ΔP between Location 2 and Location 1 (including its sign)? Ignore viscosity.

Answer 1

let
rho = 1110 kg/m^3
d1 = 5.45 cm
d2 = 2.83 cm
v1 = 2.83 m/s
let v2 is the speed of liquid at location 2

use continuity equation

A2*v2 = A1*v1

(pi*d2^2/4)*v2 = (pi*d1^2/4)*v1

v2 = v1*(d1/d2)^2

= 2.83*(5.45/2.83)^2

= 10.5 m/s

now use, Bernoulli's equation,

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

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

= (1/2)*1110*(2.83^2 - 10.5^2)

= -5.67*10^4 Pa <<<<<<<<<<---------------Answer