Posted: 10/4/2004 12:34:27 PM EDT
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Question 1: A nozzle is designed to accelerate the fluid from V1 to V2 in a linear fashion. That is V=ax+b, where a and b are constants. If the flow is constant with V1= 10 m/s at x1 = 0 and V2= 25 m/s at x2= 1 m, determine the local acceleration, convective acceleration, and acceleration of the fluid at points (1) and (2). Question 2: The Hoover Dam backs up the Colorado River and creates Lake Meade, which is approximately 115 miles long and has a surface area of appoximately 225 square miles. If during flood conditions the Colorado River flows into the lake at a rate of 45,000 cfs and the outflow from the dam is 8000 cfs, how many feet per 24-hr day will the lake level rise? thanks Scott |
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#2: Assuming the water in the lake will rise vertical and not sloped (which it would) the lake is approx 6,272,640,000 sq/feet (5280*5280*225). It is rising at a rate of 37,000 cfs or a total of 3,196,800,00 over 24 hours. 6,272,640,000/3,196,800,000 = Lake rising .5096 ft. Back to work. |
To begin with, A=15 and B=10 As for the rest, I think you need to know mass flow rate, or at least the time it took to go from X1 to X2 in order to answer this.... |
 RTFQ! 
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The equation describing the flow field is: v=15x+10. (this gives 10 m/s at x=0 and 25 m/s at x=1). It's been a few years, but I believe that local acceleration is dv/dt. In this case, it's zero because velocity of the flow field is dependant solely upon position, not time. (The flow field is steady). I believe that convective acceleration is v*dv/dx, which in this case is: (10m/s)*15/s=150 m/s^2 at point 1 (25m/s)*15/s=375 m/s^2 at point 2. total acceleration is local acceleration + convective acceleration It may seem odd that dv/dt is zero, but remember - you're looking at a fluid field, not an individual particle. How does velocity change with time in the field? A: It doesn't because velocity is a function of position only. |
Sorry, ut you are incorrect. 1) If the fluid is going faster at point 1 than point 0, then it's accelerating. 2) Acceleration of a fluid is what a nozzle does. 3) dV/dt is defined as the change in velocity per change in TIME (t). I don't know about the rest of your answer, though. Been a long time here, too! 
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Sorry, the dv/dt I used were meant to be partial derivitives. Take a look at my edited answer above and it will explain what I meant. Here's the equation for calculating acceleration of a fluid field that is a function of both time and position: dv/dt = dv/dt + Vxdv/dx (italics = partial derivative) The first term is local acceleration - it's zero because the partial derivative of velocity wrt time is zero. The second term is convective acceleration, which is acceleration due to position. It's helpful to remember the physical meaning of a partial derivative - holding all other variables constant, how does the function change with respect to one variable? If you hold position still and measure the velocity at position x=0 (or x=1), how does it change with time? A: it doesn't. On the other hand, if you hold time still, and measure the velocity at various points you find that it does change with position in the nozzle. |