Water flows steadily from the pipe shown in the figure below

Water flows steadily from the pipe shown in the figure below into the atmosphere. Viscous effects are negligible. In the last portion of the pipe, which has a diameter of 2.00 cm, the average velocity of the water is 25.0 m/s, whereas in the wider section of the pipe, which has a diameter 10.0 cm, the average velocity of the water is 1.00 m/s.

(a) Find the pressure in the centerline of the wider section of the pipe.

(b) If an open vertical tube is connected to the wider section of the pipe, how high will the level of the water be in this tube as measured from the centerline of the pipe?

Solution

Use the equation of bernouli

P1+ (1/2)*density*V1^2= P2 + (1/2)*density*V2^2

P2= 0 because it ended in the athmosphere

so we only evaluate the velocitys

density=1000 kg/m^3

P1+(1/2)*1000*1^2=(1/2)*1000^25^2

P1= 312000 Pa

so the preassure is 312 kPa

and for b) we use the same preassure that we have in A and do this

h=P/(density*gravity)

h=312000/ (1000*9.81) = 31.8 m

and the higth form the centerline is given using the diameter

31.8 m + (1/2)*(10/100 )= 31.8543 m