Water flows through a Venturi meter with a pipe diameter of 9.8 cm and a constri
ID: 1486597 • Letter: W
Question
Water flows through a Venturi meter with a pipe diameter of 9.8 cm and a constriction diameter of 5.6 cm. The U-tube manometer is partially filled with mercury. Find the flow rate of the water in the pipe of 9.8 cm diameter if the difference in the mercury level in the U-tube is 2.9 cm X L/s 118 Use the difference in height of the mercury to determine the pressure difference in the two sections. Then you can use Bernou s equation and the continuity equation to find the desired speed of water, from which you can determine the flow rate. eBookExplanation / Answer
Apply Bernoulli equation between the pipe and the throat ( constriction ) of the Venturi flow meter :
Vbar sub T = { [ - delta P/ rho ] [ 2 ] [ g sub C ] / [ 1 - B^4 ] }^1/2
B = D sub T / D sub P
B = 5.6 / 9.8 = 0.5714
1 - B^4 = 0.89337
Calculating the pressure difference
- delta P = ( R sub manometer ) ( rho sub Hg - rho sub H20 ) ( g / g sub C )
- delta p = ( 2.9 /100.0 ) (13550 - 1000) ( 9.807 / 1.000 )
- delta P = 3569.23 N. per sq. m. = 3569.23 pa.
- delta P / rho = 3200 / 1000 = 3.569 N. - m. per kg
Calculating the flow velocity,
Vbar sub T = { [ 32.00 ] [ (2.000 ) ( 1.000 0)]/ [ 0.89337 ] }^1/2
Vbar sub T = 8.4637m. per sec.
Now we apply the flow rate
A sub FT = ( pi ) ( D sub T )^2 / ( 4 )
A sub FT = ( pi ) ( 0.05600 )^2 / 4 = 0.002463 sq. m.
Q sub F = [ Vbar sub T ] [ A sub FT ]
Q sub F = [ 8.4637 ] [ 0.002463 ] = 0.01777 cu. m. per sec. =
Q sub F = 17.77 L. per sec.
mdot = [ Q sub F ] [ rho ]
mdot = [ 17.77 L. / sec. ] [1.000 kg. / L. ] = 17.77 kg. per sec.
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