Question

water flows through a pipe that gradually descends from a height of 6.78 m to the ground. near the top, the cross-sectional area is 0.4 m2, and the pipe gradually widens so that its area near the ground is 0.8 m2. water leaves the pipe at a speed of 16.8 m/s. what is the difference in the water pressure between the top and bottom of the pipe?

Answer 1

This question can easily be solved by using Bernoulli's Theorem, Pressure Difference, density, and speed of flow. Substituting the respective values the pressure difference can be found.

The difference in the water pressure between the top and the bottom of the pipe is "207.63 KPa".

Applying Bernoulli's Theorem to this situation:

$P_1+\rho gh_1+\frac{1}{2}\rho v_1^2=P_2+\rho gh_2+\frac{1}{2}\rho v_2^2\\P_2-P_1 =\Delta P= -\rho gh_2-\frac{1}{2}\rho v_2^2+\rho gh_1+\frac{1}{2}\rho v_1^2$

where,

ΔP = Pressure Difference between top and bottom = ?

$\rho$ = density of water = 1000 kg/m³

g = acceleration due to gravity = 9.81 m/s²

h₁ = heaight at top = 6.78 m

h₂ = height at bottom = 0 m

v₁ = speed of flow at top = 0 m/s (negligible)

v₂ = speed of flow at bottom = 16.8 m/s

Therefore,

$\Delta P = - (1000\ kg/m^3)(9.81\ m/s^2)(0\ m)- \frac{1}{2}(1000\ kg/m^3)(0\ m/s)^2+\frac{1}{2}(1000\ kg/m^3)(16.8\ m/s)^2+(1000\ kg/m^3)(9.81\ m/s^2)(6.78\ m)$ΔP = 141120 Pa + 66511.8 Pa

ΔP = 207631.8 Pa = 207.63 KPa

Learn more about Bernoulli's Theorem here:

brainly.com/question/13098748?referrer=searchResults

The attached picture shows Bernoulli's Theorem.