Answer:
114 kPa
Explanation:
By Bernoulli's equation when a fluid flows steadily through a pipe:
P + ρ*g*y + v² = constant in the pipe, where P is the pressure, ρ is the density of the fluid, g is the gravity acceleration (9.8 m/s²), y is the high, and v the velocity.
By the continuity equation, the liquid flow must be constant in the pipe, and then:
A1*v1 = A2*v2
Where A is the area, v is the velocity, 1 is the point 1, and 2 the point 2 in the pipe. The are is the circle area: π*(d/2)². So:
π*(0.105/2)²*9.91 = π*(0.167/2)²*v2
0.007v2 = 0.027
v2 = 3.9 m/s
Then:
P1 + ρ*g*y1 + v1² = P2 + ρ*g*y2 + v2²
ρ*g*y1 - ρ*g*y2 + v1² - v2² = P2 - P1
ρ*g*Δy + v1² - v2² = ΔP
ΔP = 1290*9.8*9.01 + 9.91² - 3.9²
ΔP = 113,987.42 Pa
ΔP = 114 kPa
