Final - winter 2011 - with solution

# Derivetherelationbetweentheforcef andthe cart

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Unformatted text preview: ed by a water jet with diameter D = 20 cm and velocity V = 100 m/sec. The cart mass is 100 kg. A force F is applied to the cart to keep its velocity U constant. U 90 V F 50 The jet is split into two parts with equal flow rates. Derive the relation between the force F and the cart velocity U; produce a qualitative plot. Find the numerical value of cart velocity U for which the power required to keep the cart velocity constant is maximized. Find the corresponding force F. [Hint: power = force x velocity] Problem 4 (20 points): See system below. Water is supplied from a large reservoir to a pipe system that includes one bend and one gate valve. The pipe system discharges to the atmosphere. L1 =10 m h = 50 m L2 = 30 m Fully open gate valve The pipe diameter is constant and equal to 10 cm. The pipe inner wall is smooth. Find the flow velocity in the pipe and the volumetric flow rate, with at least 5% precision. Problem 5 (15 points): A kid runs with a velocity of 2 m/sec, pulling and helium balloon attached to a string. The balloon can be modeled as a smooth sphere with 40 cm diameter. Neglecting the weight of the string, find the angle of the string with respect of the ground. Density of air: 1.2 kg/m3. Density of helium: 0.178 kg/m3. Viscosity of air: 2x10‐5 Pasec. Conservation of mass d m d d d 0 dt dt dt d CVS V rel dA 0 t CV Conservation of Momentum ‐ NSL t V d CV VV rel dA F N et CVS F o r stead y an d u n ifo rm : F N et _ o n _ flu id m v m v OUT IN DV g p 2V Navier‐Stokes Equation (for constant density and viscosity) Dt Cartesian components of the Navier‐Stokes Equation u u u u 2u 2 u 2 u p u v w gx 2 2 2 x y z x z t x y v v v v u v w x y z t gy 2v 2v 2v p 2 2 2 y x y z 2 2 2 w w w w u v w g z p w w w 2 x y z z y 2 z 2 t x Continuity equation (conservation of mass) for Cartesian coordinates Energy Equation 2 2 Pout Vout P V z out in in z in H pump H turbine H loss g 2g g 2 g H pump W pump mg , H turbine Wturbine mg H loss H major H min or Drag and lift coefficients: C D 2 2 Vj LV fi i i K j Di 2 g 2g FD 1 V 2A 2 , C L FL 1 V 2A 2 u v w V 0 x y z...
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## This document was uploaded on 03/07/2014 for the course ME 113 at UC Riverside.

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