Question

4 A U-Tube manometer is connected to a closed tank, shown below, containing oil a density of 800 kg/m², the pressure of the air above the oil being 6000 Pa, if the pressure at point A is 20 kPa and the manometer fluid has a relative density of 5, Assume x=0.6m. determine the following i. The depth of oil, Z ii. The differential reading, Z2 on the manometer. (5marks) Z2 Z A OIL 5 Explain about the steady and unsteady type of flow with the following of each: (i) Definition (ii) Draw its flow pattern. (iii) Discuss its type in the form of mathematical form. (iv) It's application. (2 marks) (1mark) (1 mark) (1 mark) Water flows through a pipe AB of 150 cm diameter at 2000 mm/s and then passes through a pipe BC of 6 250 cm diameter, At C, the pipe branches, Branch CD is of 1500mm diameter and carries one third of the flow in AB.The flow velocity in branch CE 250cm/s. Find the volume of flow in AB ,the velocity in BC, the velocity in CD and the diameter of CE. (5marks)

Answer 1

given is

the pressure of the air above the oil (Pair) = 6000 Pa

density of oil ($\rho$o) = 800 kg/m3

the pressure at pt.A in the oil (PA) = 20 kPa

the relative density of the manometric fluid(S.G) = 5

Z2 Iz A OIL

(i) the pressure at Pt. A can be written as

PA = Pair + $\rho$ o*g*Z1

20*1000 = 6000 + 800*9.81*Z1

Z1 = 1.784 m

(ii) pressure at a pt. below 0.6m from pt.A

P = PA + $\rho$ o*g*x

= 20000 + 800*9.81*0.6

= 24.71 kPa

now,

we know that

P = Patm + (S.G)*$\rho$w *g*Z2

24.71 = 101.325 + 5*1000*9.81*Z2

Z2 = -1.562 m