Question

A vertical pipe narrows as it carries an incompressible non-viscous fluid downwards as shown in the figure above.
If the diameter of the pipe at point 1 is 50 cm and the velocity of the fluid at point 1 is 0.67 m s−1 then what is the diameter of the pipe at point 2 such that the pressure at points 1 and 2 is the same? (to 2 s.f and in cm)

Answer 1

$$A_1v_1=A_2v_2\to 0.25d_1^2v_1=0.25d_2^2\sqrt{v_1^2+2gh}$$

$$50^2(0.67)=d_2^2\sqrt{0.67^2+2(9.8)(0.095)}$$

$$d_2=33\ cm$$