BERNOULLI’S EQUATION Fluid Flow So the decrease in elevation head can only be compensated for by an increase in pressure head. Again, the fluid is incompressible so the increase in pressure head must result in an increase in pressure. Although the Bernoulli equation has several restrictions placed upon it, there are many physical fluid problems to which it is applied.   As in the case of the conservation of mass, the Bernoulli equation may be applied to problems in which more than one flow may enter or leave the system at the same time.   Of particular note is the fact that series and parallel piping system problems are solved using the Bernoulli equation. Example: Bernoulli’s Equation Assume frictionless flow in a long, horizontal, conical pipe.  The diameter is 2.0 ft at one end and 4.0 ft at the other.   The pressure head at the smaller end is 16 ft of water.   If water flows through this cone at a rate of 125.6 ft³/sec, find the velocities at the two ends and the pressure head at the larger end. Solution: V₁ A₁v₁ v₁ V₁ A₁ v₁ 125.6 ft³ sec p(1  ft) 2 v₁ 40 ft sec v₂ V₂ A₂ v₂ 125.6 ft³ sec p(2  ft) 2 v₂ 10 ft sec z₁ v² 1 2g P_1n1 g_c g z₂ v² 2 2g P_2n2 g_c g P_2n2 g_c g P_1n1 g_c g (z₁ z₂) v² 1 v² 2 2g 16  ft 0  ft æ ç è ö ÷ ø 40 ft sec 2 æ ç è ö ÷ ø 10 ft sec 2 2^æ ç è ö ÷ ø 32.17 ft  lbm lbf  sec² 39.3  ft HT-03 Page 24 Rev. 0