32 Truelfalse Check true or false as appropriate a For horiz

32. Truelfalse. Check true or false, as appropriate (a) For horizontal flow of a liquid in a rectangular duct between parallel plates, the pressure varies linearly both in the direction of flow and in the direction normal to the plates (b For horizontal flow of a liquid in a rectangular duct between parallel plates, the boundary conditions can be taken as zero velocity at one of the plates and either zero velocity at the other plate or zero velocity gradient at the centerline (c For horizontal flow of a liquid in a rectangular duct between parallel plates, the shear stress varies from zero at the plates to a maximum at the centerline (d For horizontal flow of a liquid in a rectangular duct between parallel plates, a measurement of the pressure gradient enables the shear-stress distribution to be found (e In fluid mechanics, when integrating a partial differential equation, you get one or more constants of integration, whose values can be determined from the boundary condition(s) (f) For flows occurring between 7-0 and r = a in cylindrical coordinates, the term In r may appear in the final expression for one of the velocity components For flows in ducts and pipes, the volumetric flow rate can be obtained by differentiating the velocity profile h Natural convection is a situation whose analysis depends on not taking the density as constant everywhere

Solution

(a) False. Since, for horizontal flow of a liquid in a rectangular duct between parallel plates, the pressure varies linearly only in the direction of flow and remains constant in the direction normal to the plates.

(b) True. For horizontal flow of a liquid in a rectangular duct between parallel plates, the boudary condtions can be taken as zero velocity at one of the plates and either zero velocity at the other plate (due to maximum shear stress at the plates) or zero velocity gradient at the centerline (due to maximum velocity at the centerline).

(c) False. For horizontal flow of a liquid in a rectangular duct between parallel plates, the shear stress varies from zero at the centerline to a maxium at the plates.

(d) True.  For horizontal flow of a liquid in a rectangular duct between parallel plates, the shear-stress depends on the pressure gradient.

(e) True

(f) True

(g) False. For flow in ducts and pipes, the volumetric flow rate can be obtained by integrating the product of velocity profile and differential area.

(h) True. Natural convetion occurs due to difference in densities at various locations.