Introduction to Fluid Mechanics by Edward J. Shaughnessy Jr., Ira M. Katz, James P. Schaffer | 9780195154511 | 0195154517 | Holooly

Fluid Mechanics

Introduction to Fluid Mechanics

252 SOLVED PROBLEMS

Question: 14.9

A fully loaded aircraft weighing 900 kN has a wing area of 230 m². If the wing has the characteristics of a NACA 23012 airfoil and during takeoff operates at a 6° angle of attack, what is the required takeoff speed at sea level? What is the takeoff speed at an elevation of 2000 m? ...

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To take off, the lift force must overcome the weig...

Question: 11.11

Figure 11.13 shows a crude hurricane model in which the ﬂow is circular, and the wind speed increases linearly with radius from 0 at the center of the eye to 150 km/h at R = 50 km. Estimate the pressure difference from the eye of the hurricane to the indicated location R. ...

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Circular ﬂow implies circular streamlines with r p...

Question: 11.10

Consider a constant density ﬂuid in solid body rotation in the absence of body forces as shown in Figure 11.12. Use the Euler equations in streamline coordinates to analyze the direction of pressure change. Use the Euler equations in cylindrical coordinates to conﬁrm your ﬁndings. ...

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The velocity ﬁeld in solid body rotation is descri...

Question: 11.12

A 2D steady, constant density, inviscid ﬂow of air is described by the velocity ﬁeld u = Ax, v = −Ay, where A = 1.5 s^−1 and the coordinates are measured in feet. Find the pressure difference between a point at (1, 1, 0) and a point at (2, 2, 0). Are these two points located on the same streamline? ...

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We are asked to ﬁnd the pressure difference betwee...

Question: 11.9

The streamlines for the 2D, inviscid, constant density ﬂow over a cylinder are shown in Figure 11.8. The streamfunction for this ﬂow is given in cylindrical coordinates by ψ(r, θ) = U∞r(1− R²/r²)sinθ, where U∞ is the freestream velocity and R is the cylinder radius. If the body force is neglected, ...

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The streamfunction for a 2D constant density or in...

Question: 11.8

The steady, 2D inviscid ﬂow of an incompressible ﬂuid shown in Figure 11.7 is described by u = kx, v = −ky, w = 0, and p(x, y) = p0 − ρ(k²/2)(x² + y²), where k is a constant, p0 is the pressure at the origin, and body forces have been neglected. This inviscid ﬂow model for a constant density flow ...

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We will check that the continuity equation for an ...

Question: 11.7

In the Poiseuille ﬂow of a constant density, constant viscosity ﬂuid in a round pipe, (Figure 11.6), the velocity ﬁeld is given in cylindrical coordinates by u = vrer + vθeθ + vzez with components vr = 0, vθ = 0, and vz(r) = {[R²P(p1 − p2)]/4µL}[1−( r/RP)²]. Find the pressure distribution in this ...

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The velocity ﬁeld must satisfy the continuity equa...

Question: 11.5

Consider the ﬂow of an incompressible Newtonian ﬂuid between parallel plates with the top plate moving as shown in Figure 11.4. The velocity ﬁeld is u = U(y/h)i, where U is the speed of the moving plate and h is the gap between the plates. Find the stresses in this ﬂow. What can the momentum ...

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We are asked to ﬁnd the stresses in a given ﬂow an...

Question: 7.18

It is proposed to use high pressure water in the design of a power unit for a rotary cleaning brush. As sketched in Figure 7.30, water enters the inlet of the power unit and exits through N jets. If friction in the inlet bearing and aerodynamic drag are negligible, what is the torque available to ...

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We will choose a CV enclosing the power unit and r...

Question: 7.17

Water ﬂows steadily at 3 m/s through the vertical offset pipe bend shown in Figure 7.29. The pipe diameter is 10 cm, the upstream gage pressure is 275 kPa, and the pressure drop through the bend is estimated to be 50 kPa. Find the forces that must be exerted by each ﬂange on the pipe bend to keep ...

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We are asked to determine the forces applied to an...

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