Question

1. Atall cylindrical tank, held above ground on stilts, is partially filled with water. (See top figure). The tank has a diameter, D. At time equal to zero, a hole of diameter d is poked in the bottom of the tank, where d<< D. Let z-0 correspond to the bottom of the tank. The initial fluid height is za. Had Use Bernoulli equation to assess the velocity of the fluid as it leaves the bottom of the tank as a function of fluid a. STLTS height, z 21 b. Use the transient form of conservation of mass to assess the fluid height, function of time. Z, as a 2. Gasoline flows through the section of bent pipe shown in the middle figure. At location 1 of the pipe (which represents a cut through the pipe), the pipe diameter is 8 cm and there is a pressure sensor. Location 2 of the pipe is open to atmosphere and has a reduced diameter of 5 cm. The exit of the 1 DEFLECTOR JET ENGINE gasoline is h=12 m above the inlet. The gasoline flows at a weight flux of 120 N/s Assume no friction Determine the gage pressure at location X a. one b. Determine the x and y forces need to hold the pipe in place. Use the coordinate system provided.* 3. A deflector is placed at the exit of the jet engine as a means of braking. (See the bottom figure). The air exits the jet engine through an area of 0.4 m2 at 600°C and 900 m/s. The air is deflected uniformly around the deflector. The deflection angle, e, is 45 degrees. Determine the braking force. Use the coordinate system provided.*

Answer 1

flow A Let. Uz assume the flow it taking Prace from the bottom of the tank and at a time t. The level has reached at height į og shown in fig. Consider this of Position. consider the outlet of tank of Position 0. Assuming fluid to be ided, steady, in compressible and igrotational flow. Applying Bernoullie ean blo Point o and © Bernoullie con B + gz + x3 = constant | B +9 (z+k) to - Pe +3h + Mode - 0 Since both Points are eclosed to atmosphere P =P2 Fluid is in Compressible ; :: P=0 Solving can o we get 7+8 (244) - 34 +84 +ve Ivo - Jeez b Vg = velocity of fruid of J zgz p function of height:

5 control Volume we can write the transient equation of conservation of mass of CPr) = Porin - P Plout Since no moss is added and incompressible from Porin 50 ip = constant we get V -- Clout V = volume of tank - z(t) x area of tank V = 2(E) x TD2 2 () is de height at time t. Prout - Velocity x crea of hole - 28 2017 ~ Tid? Putting values in can olen monet - 529 2 x H - og at limite (4(E)-20) limits (4,0) Integrate the equation Be Upper limit Z(5), the for dz ig lower limit is 2(0) = Zo. For dt from t to a integrate il 2 (J2(E) - Szo) = - dog (4-0). which gives Z(A) = (520-B g +)? Height Z() as a function of time t and to