Bernoulli's Equation Along a Streamline

07/09/17 "Glory to Glod Bernaulis Equation from Euter's Equation along a stream line. Euler's equation for a particle along a streamline is gives as a/p - sg dz ds = S ( av of v.av) - as a + v av - 12P -gazz = of as f as I steady flow 2 Incompressible Inviscid Assuming 3. Along a streamline 4. dp = ap Os ds 2 V av 1/2 ( ov as a (F) = = as as av = 0 at = a ( K2) - dP ds -g dz ds ds dz d + (v2) =0 2 I dp + g ds ds I ds dp + J g dz + sa(z) 0. Integrating I J/J P + gxt V2 2 = C. Bernoulis equation P + sgz + SV 2 = C

Q horifortal Air flows steading Nazz discharging 2 At atm the The Avea the Nozzle islet is 0.1m2 the nozzle. @ Avea is 0.02 m' determine inlet to guage ext pressure the required at the nozzle produce an outlet speed of 50 m/s. Mac Number L 0.3 Gives datas: (Air is Incomplessible using equated) > Pi-fil A2= 0.02m2 A1=0-1m2 V2 50mls Islet Avea A1 0.1m2 Outlet Avea A2 - 0.02m2 Jain aim = 1.23 19/m3 hot velocity V1= ? Outlet velocity V2 50mls. To find: Guage pressure @ in inlet. P + sgx, + PV2 C Taking two point inlet and outlet P, + s ofz + svi = Petiges + PVS2 P, = P2 + SV2 (P - 12 ) + 1v/2 = PV22 2 ( P1-B) = Guage pressure at Intet. Py + PV12 = VIZZ

Now Applying to derm continuity 2/20 a you S/dv + SSV.dR=0 =0. at CN CS VIMINATE - J.V.A. + SV2A2 =0 . V2 A2 = V,A, V1 Am Di V1 V2A2 = 50x0.02 01 A1 V10 10 m/s/ Pg = SV22 - Sv2 2 1.23x502 - 1.23x102 = 2 1537.5-61.5 snls small = Pg= 1476 N/m? (Dischamic) Q the flow of air Brand a Vo bicyclist Determine Pg - 1.48 kml/m2 .Po. moving difference in pressure blw consider through still air with S velocity on vo? the 1 and 2. S P, + egfit 5x2 = B+tg + JV2 {3-31= Constant]