An apparatus to measure the speed of water is shown in the figure. It consists o
ID: 2282744 • Letter: A
Question
An apparatus to measure the speed of water is shown in the figure. It consists of a horizontal pipe with radius R1. The pipe has a constriction at the right end, open to air, with radius R2=R1/2. The pipe is connected to another vertical pipe of length L, closed at the end and filled with air.
When the speed of the water out of the constriction is v2, the level of the water in the verical pipe is h1. The density of the water is rho.
a) What is the speed of the water in the pipe under these conditions?
b) What is the pressure of the horizontal pipe?
c) What is the pressure in the air trapped in the vertical pipe?
Explanation / Answer
a) From continuity equation
we have
A1V1 = A2V2
A1 =4A2
therefore
V1= V2/4
b) pressure in horizontal pipe = P0 + ( density * g * h1)
where P0 = pressure in the air entrapped vertical pipe
c) P0 = pressure in air entrapped pipe