Quiz 4 Solutions – Bernoulli Equation II

Quiz Four Solutions - Bernoulli Equation II JP4 fuel (SG = 0.77) flows through the Venturi meter shown in the figure at the right. The inlet velocity in the pipe is 15 ft/s. If viscous effects are negligible, determine the elevation. h, of the fuel in the open tube connected to the throat of the Venturi area. (Problem and Figure P3.68 taken from Munson et al, Fluid Mechanics.) Apply the Bernoulli equation for incompressible. inviscid flows, shown below, between two points (1) and (2) along a streamline in the center of the pipe 42) JP-4 fuel 6 in. - 15 ms - 4-0 2g The diagram shows that the elevation difference, z2 - 2, = 8 in = 0.8887 ft. We can apply the continuity equation between points (1) and (2) where we assume that the JP4 density does not change. This gives 1, 4 - 1,1, → V.2-V ED. 4 Since the diameter at point 2 is the same as the inlet diameter where V = 15 m/s, the continuity equation tells us that V2 = 15 fu/s as well. Thus we can find the value of V, from the diameter- squared ratio. 33.75 A 4 in Pressures so than the pressure 2 he top orin to ta re tre a wee piuould fe on tree fluid-static equation pa = 7h2 = (® ff). where y is the specific weight of the JP4. We can substitute this expression for pa into our Bernoulli equation along with the values found above: 22 - 2, = 0.6687 ft. V, = 33.76 ft/s. and V, = 15 ft/s. This gives the Bernoulli equation as 15 f 33.75 f 2321743 Calculating the velocity term and rearranging the numerical equation gives. 0.6667 A + 6 f - E - 14.205 # = 0 → 4 = -7538 f The manometer at the Venturi throat is open to the atmosphere so the pressure on the open arm is zero. Since the bottom of the displacement h is at the same level as the open arm of the manometer the pressure at this level on the left side of the manometer is zero. This must be less than the pressure at point 1, pr. by the specific weight, y. times the height, h. that we are trying to find. This gives the manometer equation as follows. p, + 1h= 0 → h=-A =-(-7.538#) We see that the manometer height is poly which is the same quantity whose numerical value we found as -7.538 ft from Bernoulli's equation. This gives us our answer for the manometer height: h = 7.538 ft What would your answer be if the fluid were water? The above analysis shows that the specific gravity does not play a role in the solution so the answer would be the same. h = 7.538 fil if the fluid were water.