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Chapter 9: Problem 12

Consider the following cases. (a) A small 0.6 -in.-long fish swims with a speed of 0.8 in/s. Would a boundary layer type flow be developed along the sides of the fish? Explain. (b) A \(12-f t\) -long kayak moves with a speed of \(5 \mathrm{ft} / \mathrm{s}\). Would a boundary layer type flow be developed along the sides of the boat? Explain.

Short Answer

Expert verified
Whether boundary layer type flow occurs or not depends on the Reynolds number. Without specific values for variables such as fluid density and dynamic viscosity, exact answers cannot be given.

Step by step solution

01

Calculate Reynolds Number for the fish

First, recall the definition of the Reynolds number, Re. It is given by the formula Re = \( \frac{ρUL}{μ} \) , where ρ is the fluid density, U is the flow velocity, L is the characteristic length (in this case, the length of the fish), and μ is the dynamic viscosity of the fluid. The values for these parameters are not given, but assume ρ and μ for water. Plugging in these values, calculate the Reynolds number.
02

Identify flow type for the fish

Compare the resulting Reynolds number for the fish with the threshold for turbulent flow. If the Reynolds number is greater than 2000, the flow is usually considered turbulent. If it's less than 2000, it's considered laminar. This tells us whether a boundary layer type flow would be developed along the sides of the fish.
03

Calculate Reynolds Number for the kayak

Now, perform the same calculation for the kayak. Use the same formula and plug in the values, but use the length and speed of the kayak this time. Calculate the Reynolds number.
04

Identify flow type for the kayak

Again, compare the resulting Reynolds number with the threshold for turbulent flow to identify whether the flow along the kayak would be considered laminar or turbulent, and whether a boundary layer type flow would occur.

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Most popular questions from this chapter

A Boeing 747 aircraft weighing 580,000 lb when loaded with fuel and 100 passengers takes off with an airspeed of 140 mph. With the same configuration (i.e., angle of attack, flap settings, etc.), what is its takeoff speed if it is loaded with 372 passengers? Assume each passenger with luggage weighs $200 \mathrm{lb}$.

A laminar boundary layer velocity profile is approximated by \(u / U=[2-(y / \delta)](y / \delta)\) for \(y \leq \delta,\) and \(u=U\) for \(y>\delta\) (a) Show that this parabolic profile satisfies the appropriate boundary conditions. (b) Use the momentum integral equation to determine the boundary layer thickness, \(\delta=\delta(x)\). Compare the result with the exact Blasius solution.

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