The horizontal pipe shown in the figure Figure 1 has a cross

The horizontal pipe, shown in the figure (Figure 1), has a cross-sectional area of 40.0 cm2 at the wider portions and 10.0 cm2 at the constriction. Water is flowing in the pipe, and the discharge from the pipe is 6.00times10-3 m3/s (6.00L/s). The density of mercury is rhoHg = 13.6timesl03kg/m3 and the density of water is rhow = 1.00times103kg/m3. What is the difference in height between the mercury columns in the U-shaped tube?

Solution

From Continuity equations

A₁V₁=A₂V₂

40*V₁=10*6

V₁=1.5 m/s

From Bernoull\'s equation

P₁+(1/2)pV₁²+pgy =P₂+(1/2)pV₂²+pgy

P₁-P₂ =(1/2)p[V₂²-V₁²] =(1/2)*1000*[6²-1.5²]

P₁-P₂=16875 pa

Since

P₁-P₂  = (p_mercury-p)gh =(13600-1000)*9.8*h

16875 =12600*9.8*h

h=0.1366 m or 13.66 cm