Water of constant density The solution is- Can someone show me how to.docx

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Water of constant density The solution is: Can someone show me how to obtain this? (rho) (Di) (pi) (.8 Di) F = -1.99 rho Q2/D2 I + (pi piD2 i/4 +rhoQ2/pi D 2 i)j L = pi/rho - 1.17 Q2/D 4 I To = 1.9 rho Q2 L/D 2 I (k) Solution Mass flow rate m = rho*Q where Q = pi/4*Di^2*Vi m = rho*pi/4*Di^2 *Vi Also, Q = Ai*Vi = Ae*Ve Q = pi/4 * Di^2 *Vi = pi/4 * De^2 *Ve Ve = Vi*(Di / De)^2 Ve = Vi*(1 / 0.8)^2 Ve = 1.5625*Vi Pi + 1/2*rho*Vi^2 = Pe + 1/2*rho*Ve^2 But Pe = 0 (atmospheric) Hence, Pi + 1/2*rho*Vi^2 = 1/2*rho*(1.5625*Vi)^2 Pi = 0.7207*rho*Vi^2 Vi = 1.178*sqrt (Pi / rho) Force Fx = -m*Ve = -rho*Q*Ve = -rho*Q*(4Q / (pi*De^2)) = -rho*Q^2 *(4/pi)/(0.8*Di)^2 = -1.99*rho*Q^2 / Di^2 Force Fy = pi*Ai + m*Vi Fy = Pi*(pi/4)*Di^2 + rho*Q*Vi Fy = Pi*(pi/4)*Di^2 + rho*Q*Q / [(pi/4)*Di^2] Fy = Pi*(pi/4)*Di^2 + 4*rho*Q^2 / (pi*Di^2) Thus, Total F = Fx i + Fy j F = -1.99*rho*Q^2 / Di^2 i + [Pi*(pi/4)*Di^2 + 4*rho*Q^2 / (pi*Di^2)] j .

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But Pe = 0 (atmospheric)
Hence, Pi + 1/2*rho*Vi^2 = 1/2*rho*(1.5625*Vi)^2
Pi = 0.7207*rho*Vi^2
Vi = 1.178*sqrt (Pi / rho)
Force Fx = -m*Ve = -rho*Q*Ve
= -rho*Q*(4Q / (pi*De^2))
= -rho*Q^2 *(4/pi)/(0.8*Di)^2
= -1.99*rho*Q^2 / Di^2
Force Fy = pi*Ai + m*Vi
Fy = Pi*(pi/4)*Di^2 + rho*Q*Vi
Fy = Pi*(pi/4)*Di^2 + rho*Q*Q / [(pi/4)*Di^2]
Fy = Pi*(pi/4)*Di^2 + 4*rho*Q^2 / (pi*Di^2)
Thus, Total F = Fx i + Fy j
F = -1.99*rho*Q^2 / Di^2 i + [Pi*(pi/4)*Di^2 + 4*rho*Q^2 / (pi*Di^2)] j

Water of constant density The solution is- Can someone show me how to.docx

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