A fishnet is made of 1-mm-diameter strings knotted into2 x 2 cm squares. Estimate the horsepower required totow 300 ft 2 of this netting at 3 kn in seawater at 20 ° C. Thenet plane is normal to the flow direction.

Consider the boundary layer over a flat plate at 45° angle as shown. The exact flow field in this configuration is described by the Falkner-Skan similarity solution with n = 1/3 (see Figure 10.8 of the textbook, the Falkner-Skan profile chart). The objective is to find the approximate solution to this problem using the Thwaites method and calculate its error. Ve 11/4 Assume that for this approximate solution the free stream velocity is U₂(x) = ax" where a is an unknown constants and n = 1/3. Use the Thwaites method to find the momentum 0/x and 8*/x displacement thicknesses as well as the friction coefficient cf = 0.5, as functions of Re₂ = Uer/v, where is the shear stress at the wall. (No need to interpolate the Thwaites method table values; you can pick the nearest numbers.) Using the Falkner-Skan profile chart approximate the friction coefficient c; (by estimating the slope of the corresponding velocity profile at the wall). How does this value compare with your prediction in part…

By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane. expressions for velocity are: v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cos⁡θ v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sin⁡θ Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.

A ship 50 m long, with a wetted area of 800 m2, has the hullshape tested in Fig. There are no bow or stern bulbs.The total propulsive power available is 1 MW. For seawaterat 20°C, plot the ship’s velocity V kn versus power Pfor 0 < P <1 MW. What is the most efficient setting?

Rain water is flowing through an inclined plane under gravity as shown in figure. A thin layer of thickness h is formed over the plate. An upward wind flow that exerts a shear stress on the upper surface (y = h) of the liquid layer. The wind flow tends to push the rain layer upward while gravity pulls the layer downward Write continuity and and Navier-Stokes equations to model this flow field. (Assume the flow is fully developed) Obtain expressions for the liquid velocity profile, the shear stress distribution, the volume flow rate, and the the expression for the thickness h of the liquid layer for which there is no net volume flow along the roof