Fluid of density 885kg/m^3 enters a 30cm-long 1cm-diameter tube with uniform ste
ID: 1717998 • Letter: F
Question
Fluid of density 885kg/m^3 enters a 30cm-long 1cm-diameter tube with uniform steady velocity of 1.2m/s. The inlet pressure is 2540Pa greater than the pressure at a distance L_1=10cm. At L_1 the flow is fully laminar, i.e. the velocity becomes parabolic and remains that way to the exit of the tube. Determine the maximum speed at L_1 and the magnitude of the viscous (frictional) force exerted by the tube walls on the flowing fluid from inlet to L_1. What is the wall average shear stress, from inlet to L_1? (Recall - per our discussion in class regarding average speed - that an area average of a quantity, let's say quantity X can be determined by where A is an appropriately selected area.)Explanation / Answer
Some issues with uploading the pic. Please note the approach.
Use Hage-Poisseuille's equation to obtain the volumetric flow rate Q, from where you can calculate the velocity. All the other parameters of the equation are given, including the differential pressure.
Note that the maximum speed in a tube, at any point in space and time will be at the centre (of the parabola).
Magnitude of Viscous force can be calculated using shear. Calculate shear as {delta (velocity)/ delta (displacement)}. .From there, after getting the value of shear, obtain viscous force using {(shear)*(CS Area)}.
To find the wall average shear stress from inlet to L1, use the hint as given. Select the area of the wall as the (Length* small Breadth)
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