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# hw_7 - ME 152A(Fall 2008 m Prof Sumita fennathur HW#7 L...

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Unformatted text preview: ME 152A (Fall 2008) m Prof. Sumita fennathur HW #7 L Blue and yellow streams of paint Em 700kg1/1 3 and viscosity 1000 times greater than water (I £1000 w) enters a pipe at lmp‘ . Will paint exit the 8m long pipe as green paint, or separate streams of blue and yellow paint? Assume the pipe is 3cm diameter. Repeat problem if the paint were “thinned” (assume It? stays the same). Blue —* W ..... Green? 3 cm -+ Yellow H+ l m w W! 8'11“; 2. Water ﬂows at a rate of 40 liters per minute in a new, horizontal 20m diameter galvanized iron i e. Determine the ressure radient, 32, along the pipe. P P P g l 3. fuel/C)2 The ﬁgure shows a rocket engine mounted "' P esp on a stationary test bed. The rocket is fueled l “m by a long mixture of liquid alcohol and vs liquid air supplied via a flexible pipe which PM,“ transmits no force and is operated in steady "’2 state. The mass flow rate of the ﬁtelgl) 2 mixture is n‘z. At the exit plane the gas velocity is V; and the pressure is pg. Note that p313 because the rocket exit is supersonic. a) in terms of the exit area A, and the other speciﬁed quantities, derive an expression for the thrust force exerted by the rocket on its support if the rocket is free standing, and the jet does not include signiﬁcant air flow around the body. ‘0) Because of noise complaints from neighbors, a silencer is installed around thejet as shown below. Large amounts of air are drawn by the jet into the silencer tunnel, and there is now a noticeable wind in the neighborhood of the rocket body. Note— since flow in nozzle is supersonic, the silencer does not affect the exit plane velocity or pressure. With the silencer installed, the thrust force measured at the rocket base by greater or smaller than that in part a? Silencer 4. A high—speed test vehicle with initial velocity K, is to be brought quickly to rest on level ground by tiring a rocket in the direction of motion. 'iThe rocket burns solid propellant at a mass rate mags / ) and ejects gas at a speed V relative to itself. The total mass of :3 propellant burned during the rocket ﬁring is small compared with the initial mass M of the system as a Whole. Neglecting friction between the wheels and the ground, as well as air drag, obtain an expression for the duration that the rocket must be fired in order to bring the vehicle to rest. For simplicity, assume that the pressure at the rocket exit is atmosphere (Note: this may not be realistic if the rocket tires at sonic or supersonic speed). Givens: 1141633 V m 5. (Extra Credit) After its second booster has been ﬁred, a space vehicle ﬁnds Wt) itself outside the earth’s atmosphere, moving vertically upward at a speed of VD against gravity g. Its total mass at that point is M0. At t2 0, the vehicle’s third stage is turned on and the rocket burns propellant at a mass ﬂow rate 1521ch / ), ejecting {EQ gas from the exit plane (Area A2) at a speed I”; relative to the rocket. Show that if the gravitational acceleration remains essentially constant at the vehicle during the rocket ﬁring, the velocity Vt( ) of the vehicle after time 2: will be given by, Wt) — V0 W Va. In[Mg/M(r)] ~ gt Where Mt( ) is the mass of the system at time 1‘. Assume that l l 1 although the pressure of the gas at the rocket exit plane is p, (the rocket exhaust is supersonic, so the pressure exit will not balance with zero pressure in space) but the effect of this finite exit plane pressure on thrust is negligible. ...
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hw_7 - ME 152A(Fall 2008 m Prof Sumita fennathur HW#7 L...

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