Answer to Question #161002 in Mechanics | Relativity for Ermus Ken

Question

Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000 Pa. At the nozzle the pressure decreases to atmospheric pressure (101300 Pa), there is no change in height. Use the Bernoulli equation to calculate the velocity of the water exiting the nozzle. (Hint: The density of water is 1000 kg/m³ and gravity g is 9.8 m/s². Pay attention to units!)

Answer 1

Let's write the Bernoulli equation:

$$\dfrac{1}{2}\rho v_1^2+\rho gh_1+p_1=\dfrac{1}{2}\rho v_2^2+\rho gh_2+p_2.$$

Since there is no change in height ($h_1=h_2$) the equation takes the next form:

$$\dfrac{1}{2}\rho v_1^2+p_1=\dfrac{1}{2}\rho v_2^2+p_2,$$ $$v_2=\sqrt{\dfrac{\dfrac{1}{2}\rho v_1^2+p_1-p_2}{\dfrac{1}{2}\rho}},$$

$v_2=\sqrt{\dfrac{\dfrac{1}{2}\cdot1000\ \dfrac{kg}{m^3}\cdot(1.0\ \dfrac{m}{s})^2+2\cdot10^5\ Pa-1.013\cdot10^5\ Pa}{\dfrac{1}{2}\cdot1000\ \dfrac{kg}{m^3}}}=14.0\ \dfrac{m}{s}.$