Question

a pipeline has an initial height of 0.0 m having a pressure of 150 Pa and velocity of 5.0 m/s. what happen to the pressure if thr velocity is now at 10.0 m/s at a height of 2 meter?

Answer 1

We can find the pressure at a height of 2 meter from the Bernoulli's equation:

$$\dfrac{1}{2}\rho v_1^2+\rho gh_1+p_1=\dfrac{1}{2}\rho v_2^2+\rho gh_2+p_2,$$ $$p_2=\dfrac{1}{2}\rho(v_1^2-v_2^2)+\rho g(h_1-h_2)+p_1,$$

$p_2=\dfrac{1}{2}\times1000\ \dfrac{kg}{m^3}\times((5\ \dfrac{m}{s})^2-(10\ \dfrac{m}{s})^2)+1000\ \dfrac{kg}{m^3}\times9.8\ \dfrac{m}{s^2}\times(0\ m-2\ m)+150000\ Pa=92.900\ Pa.$