The horizontal pipe, shown in the figure (Figure 1), has a cross-sectional area
ID: 1380511 • Letter: T
Question
The horizontal pipe, shown in the figure (Figure 1), has a cross-sectional area of 40.0 cm^2 at the wider portions and 10.0 cm^2 at the constriction. Water is flowing in the pipe, and the discharge from the pipe is 6.00 x 10^-3 m^3 /s (6.00 L/s). The density of mercury is P Hg = 13.6 x 10 kg/m^3 and the density of water is P w = 1.00 x 10^3 kg/m^3. Part C What is the pressure difference between these portions? Part D What is the difference in height between the mercury columns in the U-shaped tube?Explanation / Answer
The flow rate
V = A1 v1
v1 = ( 6.00*10^ -3 m ^3 /s ) / (40*10^ -4 m ^2 )
= 1.5 m/s
From the equation of continuity
v2 = A1 v1 / A2
= ( 40*10^ -4 m ^2 ) ( 1.5 m/s ) / ( 10*10^ -4 m ^2 )
= 6 m/s
The bernoullis equation is
P2 - P1 = ( 1/2) rho (v_2^2 - v_1 ^2 )
= ( 0. 5 ) ( 1000 kg / m^3 ) ( 36 - ( 1.5 m/s ) ^2 )
=16875 Pa
b)
The height difference is
delta P = ( rho ) _hg g ( delta h)
(delta h ) = (16875 Pa ) / (13.6*10^ 3 kg / m^3 ) ( 9.8 m/s^2 )
= 0.126 m
= 12.6 cm
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