Answer:
Pressure change in pipe is 766.96 N/m²
Explanation:
The continuity equation is stated below,
AV = Q
A1V1 = A2V2
Where A is the cross-sectional area, V is the velocity and Q is the fluid flow rate.
To calculate the inlet velocity of the pipe,
V1 = Q/A1
V1 = Q/(π x d1²)
d1 is the inlet diameter of the pipe
Substituting values,
V1 = 0.011/(π x 1/4 x 0.06²)
V1 = 3.89 ms-¹
To determine the outlet velocity,
V2 = Q/A2
d2 is the outlet diameter of pipe
V2 = 0.011/(π x 1/4 x 0.11²)
V2 = 1.157 ms-²
Applying Bernoulli's equation for steady flow between the points,
P1/pg + a1(V1²/2g) + z1 + hp = P2/pg + a2(V2²/2g) + z2 + ht + hL
Collecting like terms,
The kinetic energy correction factor, a = a1 = a2
a((V1² - V2²)/2g) - hL = (P2 - P1)/pg
apg((V1² - V2²)/2g) - hLpg = P2 - P1
ap((V1² - V2²)/2) - hLpg = ∆P
p - density of water, g is the acceleration due to gravity and hL is the head loss due to friction in pipe.
Substituting values,
a = 1.05, p = 1000kg/m³, g = 9.81m/s², hL = 0.66m
∆P = (1000)(1.05)((3.89² - 1.157²)/2) - (0.66 x 1000 x 9.81)
∆P = 7241.56 - 6474.6
∆P = 766.96 N/m²
