The law of the wake in the turbulent boundary layer is a concept introduced to describe the mean-velocity profile in turbulent flows. It is proposed that the profile can be represented as a linear combination of two universal functions: the law of the wall and the law of the wake. The law of the wall is well-known and describes the mean-velocity profile near the wall, while the law of the wake is characterized by the profile at a point of separation or reattachment. These functions are established empirically based on mean-velocity profile measurements and are not tied to any hypothetical mechanism of turbulence. Using these functions, the shearing-stress field for various flows is computed and compared with experimental data. The development of a turbulent boundary layer is interpreted in terms of an equivalent wake profile, which represents the large-eddy structure and is constrained by inertia. The presence of a wall introduces additional constraints through viscosity, which is manifested in the sublayer flow and the logarithmic profile near the wall. The law of the wake is suggested to be useful for yawed or three-dimensional flows, where the wall and wake components are considered as vector quantities. The wall component is defined in the direction of the surface shearing stress, and the wake component is found to be nearly parallel to the gradient of the pressure in some cases. The law of the wall is derived from observations of pipe flow and is expressed as a universal similarity law for turbulent flow past a smooth surface. The law of the wall is validated by experimental data and is used to describe the mean-velocity profile in various flows. The defect law and the equilibrium boundary layer are also discussed, with the defect law being a relationship that describes the momentum defect in the mean-velocity profile. The equilibrium boundary layer is characterized by a constant parameter, and the defect law is shown to be insensitive to wall roughness. The wake hypothesis is introduced as a second universal function in the mean-velocity profile, which is used to describe the departure of the mean-velocity profile from the logarithmic law of the wall. The wake function is normalized and is shown to be a universal function that applies to various flows. The wake function is tested against experimental data and is found to be a useful concept for describing the mean-velocity profile in various flows. The wake hypothesis is also applied to flows approaching or recovering from separation, as well as to yawed flows and flows that are actually separated from the adjacent wall. The equations of mean motion are discussed, and the turbulent shearing stress is shown to be related to the mean velocity through the equations of mean motion. The equations of mean motion are used to compute the shearing-stress profile and are validated against experimental data. The results show that the equations of mean motion provide a valid relationship between shearing stress and mean velocity, and the analytic representation of the mean-velocity profile is used to compute the shearing-stress profile. The results are consistent with experimental data and support the hypothesis of a universal lawThe law of the wake in the turbulent boundary layer is a concept introduced to describe the mean-velocity profile in turbulent flows. It is proposed that the profile can be represented as a linear combination of two universal functions: the law of the wall and the law of the wake. The law of the wall is well-known and describes the mean-velocity profile near the wall, while the law of the wake is characterized by the profile at a point of separation or reattachment. These functions are established empirically based on mean-velocity profile measurements and are not tied to any hypothetical mechanism of turbulence. Using these functions, the shearing-stress field for various flows is computed and compared with experimental data. The development of a turbulent boundary layer is interpreted in terms of an equivalent wake profile, which represents the large-eddy structure and is constrained by inertia. The presence of a wall introduces additional constraints through viscosity, which is manifested in the sublayer flow and the logarithmic profile near the wall. The law of the wake is suggested to be useful for yawed or three-dimensional flows, where the wall and wake components are considered as vector quantities. The wall component is defined in the direction of the surface shearing stress, and the wake component is found to be nearly parallel to the gradient of the pressure in some cases. The law of the wall is derived from observations of pipe flow and is expressed as a universal similarity law for turbulent flow past a smooth surface. The law of the wall is validated by experimental data and is used to describe the mean-velocity profile in various flows. The defect law and the equilibrium boundary layer are also discussed, with the defect law being a relationship that describes the momentum defect in the mean-velocity profile. The equilibrium boundary layer is characterized by a constant parameter, and the defect law is shown to be insensitive to wall roughness. The wake hypothesis is introduced as a second universal function in the mean-velocity profile, which is used to describe the departure of the mean-velocity profile from the logarithmic law of the wall. The wake function is normalized and is shown to be a universal function that applies to various flows. The wake function is tested against experimental data and is found to be a useful concept for describing the mean-velocity profile in various flows. The wake hypothesis is also applied to flows approaching or recovering from separation, as well as to yawed flows and flows that are actually separated from the adjacent wall. The equations of mean motion are discussed, and the turbulent shearing stress is shown to be related to the mean velocity through the equations of mean motion. The equations of mean motion are used to compute the shearing-stress profile and are validated against experimental data. The results show that the equations of mean motion provide a valid relationship between shearing stress and mean velocity, and the analytic representation of the mean-velocity profile is used to compute the shearing-stress profile. The results are consistent with experimental data and support the hypothesis of a universal law