Fluid mechanics

DifferentialManometer (Numericals 1):

1. A U-tube monometer is used to measure the pressure of oil (specific gravity 0.85) flowing in a pipe line. It's left end connected to pipe and right limb is open to the atmosphere. The centre of pipe is 100 mm below the level of mercury in the right limb. If the difference of mercury level in the two line is 160 mm, then determine the head and pressure.

Solution:        

h = 13.6 x 160 x 10^-3x 0.85 x60 x 10^-3
                           = 2176 x 10^-3 x 51.00 x 10^-3
                           = (2176-51) x 10^-3
                           = 2125 x 10^-3
                           = 2.125 m
                        P = ρgh
                           = 1000 x 9.81 x2.125  

                                 P= 20846.25 N/m² 

2. A U-tube monometer containing mercury was used to find the negative pressure in the

pipe. The right limb was open to the atmosphere; find the vacuum pressure in pipe if the

difference of mercury level in two pipes is 100 mm and height of water in the left limb from

the centre of pipe was found to 40 mm.

Solution:

h = - (h₁S₁+ h₂S₂)

= - (40x1+100x13.6) x 10^-3

 = - (40+1360) x 10^-3

 = -1400 x 10^-3

 = -1.4 m

P = ρgh

P= 13734 N/m²

3.A simple U-tube manometer containing mercury is connected to a pipe in which an oil of

specific gravity 0.80 is flowing. The pressure in the pipe is vacuum. The other end of the

manometer is open to atmosphere, find the vacuum pressure in pipe if the difference of

mercury level in two limbs is 200 mm and height of oil in left end from the centre of pipe is

150 mm below.

Solution:

            h = h₂S₂- h₁S₁
               = (200 x 13.6 x 150 x 0.8) x10^-3
               = (2720-120) x10^-3
               = 2600 x 10^-3
               = 2.6 m                    
            P = ρgh
               = 800 x 9.81 x 2.6

            P= 20404.8 N/m²