2 Use the mass continuity equation to derive an expression for the vertical velocity at the top of aplanetary boundary layer of fixed depth HB in which the zonal wind is u(x)=U, cos(2xx/L). U.and L are constant with time and height in the boundary layer. There is no motion in the ydirection and the surface is strictly horizontal. Neglect variations in density.

for the above question the answer is Zero(0)

Answered: Use the mass continuity equation to…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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can someone explain why P is a function if time only for this question
From the laminar boundary layer the velocity distributions given below, find the momentum thickness θ, boundary layer thickness δ, wall shear stress τw, skin friction coefficient Cf , and displacement thickness δ*1. A linear profile, u(x, y) = a + by 2. von K ́arm ́an’s second-order, parabolic profile,u(x, y) = a + by + cy2 3. A third-order, cubic function,u(x, y) = a + by + cy2+ dy3 4. Pohlhausen’s fourth-order, quartic profile,u(x, y) = a + by + cy2+ dy3+ ey4 5. A sinusoidal profile,u = U sin (π/2*y/δ)
Algebraic equations such as Bernoulli's relation, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди ди ap ат ри — + pu Әх + pg: + дх ày ду where T is the boundary-layer shear stress and g, is the com- ponent of gravity in the x direction. Is this equation dimen- sionally consistent? Can you draw a general conclusion?
Find the vorticity of the fluid motion for the given velocity com- ponents. KINEMATICS OF FLUIDS (a) u A(x + y), v = - A(x + y) (b) u = 2Axz, (c) u Ay²+ By + C, v = A(c² + x² - z²) 1)=0
Two infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at speed V, as inFig. There is a fluid of viscosity μ and constant pressurebetween the plates. Neglecting gravity and assumingincompressible turbulent flow u(y) between the plates, usethe logarithmic law and appropriate boundary conditions toderive a formula for dimensionless wall shear stress versusdimensionless plate velocity. Sketch a typical shape of theprofile u(y).
Q5. A deep pool of oil having kinematic viscosity 3.45x10 m²/s is resting over a flat plate. The plate is suddenly set into motion with velocity 5 cm/s at time t-0. What will be the boundary layer thickness after 10s when the plate was set in motion?
1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?
Q2 Fluid mechanics With respect to the stream function, develop the superposition for two cases: - Uniform + Dipole - Uniform + Dipole (a->0)
Q4) Define the boundary layer, then find the thickness of boundary layer, shear stress, drag force and coefficiet of drag in terms of Re for the velocity profile of laminar boundary layer u/U=4(y/8)-6(y/8)5. Calcate the boundary layer thickness and drag force if the air flows over a sharp edged flat plate 1m long and 0.5m wide at a velocity 0.9m/s, the air density 1.23 kg/m³ and the kinematic viscosity is 1.46*10-5 m/s².
If a vertical wall at temperature T, is surrounded by a fluid at temperature T, a natural convection boundary layer flow will form. For laminar flow, the momentum equation is au ди. p(u-+ v) = PB(T – T)g + µ- ди ay to be solved, along with continuity and energy, for (u, v, T) with appropriate boundary conditions. The quantity B is the thermal expansion coefficient of the fluid. Use p, g, L, and (Tw- To) to nondimensionalize this equation. Note that there is no “stream" velocity in this type of flow.
1. In Class, we used a small differential volume to derive the expression for momentum thickness. Here, use a control volume approach, as shown in the figure, to derive the definition of momentum thickness, 0, for flow over a flat plate. zero shear stress, constant pressure, no through flow h> 8 no slip, ,#0
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