Question

Water flowing out of a horizontal pipe emerges through a nozzle. the radius of the pipe is 1.7 cm, and the radius of the nozzle is 0.46 cm. the speed of the water in the pipe is 0.45 m/s. treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe.

Answer 1

By equation of continuity we can find the speed of flow through nozzle

[tex]A_1v_1 = A_2v_2[\tex]

[tex]\pi*1.7^2*0.45 = \pi*.46^2*v_2[\tex]

[tex]\pi*1.7^2*0.45 = \pi*.46^2*v_2[\tex]

[tex]v_2 = 6.15 m/s[\tex]

Now we can use equation of continuity to find the pressure

[tex]P_1 + 0.5 \rho v_1^2 = P_2 + 0.5 \rho v_2^2[\tex]

At exit through nozzle pressure will be same as atmospheric pressure

[tex]P_1 + 0.5 *1000*0.45^2 = 1.01*10^5 + 0.5*1000*6.15^2[\tex]

[tex]P_1 = 1.2* 10^5 Pa[\tex]