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Unformatted text preview: 2f24r’2009
MAE 101 A
WINTER 2009 Professor Juan C. Lasheras
Midterm #2 PROBLEM 1. EXTRA CREDIT (10 points)
Consider a steady flow of water through a device shOWn in ﬁgure. The three cross
sectional areas are equal A.= A2= A3=A. The volumetric ﬂow rate in section l is Q1 and the mass flow rate in section 2 is m,.
Calculate the velocity of the water ﬂowing through section 3 as a function of ,0,A,éi,andrnz. xii-3
—-«-—> * KT ’1 “Z PROBLEM 2. (25 points} .
Two water jets of equal circular cross sections, A1=A2 and speed V1=V2 strike each
other at 90° angle, as shOWn in the ﬁgure. After striking each other the jets merge into
a single jet with speed V and direction 6.
a) Neglecting the effect of gravity, calculate V and B. V
b) Calculate V and 8 if V1=1 Oﬁfs and D1=0.I ft. ' PROBLEM 3 (25 points)
Water flows steadily through a 90° reducing elbow as shown in the ﬁgure. At the inlet
of the elbow the absolute pressure of the fluid is P] and the cross sectional area A.. At
the outlet of the elbow the cross sectional area is A2 and the velocity is V2. The elbow
discharges to the atmosphere (Pg: Pa). a) Determine the force required to hold the elbow in place. b) Calculate the force when Pi= 221 kPa (absolute), A1=0.01 m2, A2=0.002S m2
and V2=16 mls. __ _ __L
PROBLEM 4 (25 points) Water ﬂows steadily through a pipe bend of diameter D as shown in ﬁgure. The
pressure at the entrance and exit are P] and P2 reSpectively‘
a) Compute the torque T at the point B necessary to keep the pipe from rotating for a volumetric ﬂow rate b) Calculate T if Q=30 gala’min, D=0.?5 in, P1= 30 lbffin2 and [33:24 lb’ffin2 PROBLEM 5 (25 points)
Air-ﬂows steadily from a tank through a horizontal hose of diameter D and exits to the atmosphere from a nozzle of diameter d, as shown in ﬁgure. The pressure in the
tank remains constant at P1(gage pressure) and the exit is at atmospheric conditions, at
standard temperature and pressure. a) Determine the ﬂow rate Q assuming incrompressible ﬂow and that viscous
effects can be neglected. b) Find £2 for mass m, d=0.01 m, P1: 3.0 kPa (gage).
0) Calculate the pressure in the hose, P2. 1 L PM (It? 4L .
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