The flow rate of a steady flow of viscoelastic fluid under a constant pressure gradient in a toroidal pipe of circular cross-section is analytically solved with the White-Metzner constitutive equation by a perturbation method. It is examined how the shear thinning viscosity and elasticity affect the flow rate of the fluid at high shear rate to which former analyses could not be applied.
The analysis shows that the characteristics of the flow in a curved pipe are determined not only by the Dean number but also by the non-dimensional value W_e /√Rwhere W_e is the Weissenberg number and R is the ratio of toroidal radius to cross-sectional one. The results calculated for the ratio f_r of the flow rate in a toroidal pipe to that in a straight pipe under the same pressure gradient in the flow direction at low Reynolds number are asfollows :
(1) In the case of power law fluid in which W_e is zero, f_r decreases with increasing the Reynolds number R_e and with decreasing the viscosity index n. Thus, the resistance in a curved pipe is higher than that in a straight pipe.
(2) The larger W_e gives the larger f_r, thus the pipe resistance is smaller.
(3) The larger R_e and the smaller n give the larger degree of increment of f_r with increasing W_e.
(4) The effect of the elasticity index s, representing the shear thinning elasticity, on f_r is insignificant unless the value of n is small.

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This paper aims to investigate experimentally the effect of the needle thread slipped out of a rotating hook on the tightening tension of a industrial single-needle lockstitch sewing machine. For this purpose, the behaviors of the threads slipped out of the rotating hook are photographically observed, and the needle thread tentions generated at the same time are measured. A rotating hook, manufactured by Hirose Manufacturing Co. Ltd., model HSL-B is used, which is provided with a rotating hook section jib. The sewing speed is 2, 250 spm, and the sewing threads chosen as the experimental factor are cotton, polyester and nylon filament sewing threads.
The experimental investigation mentioned above revealed that the behaviors of the needle thread slipped out of the rotating hook are determined depending on the elongation properties of the sewing threads.
If the cotton thread of less elongation is used as sewing threads, the needle thread first slips out of the jip and then slips out of the 'rotating hook bobbin case holder position bracket.' This is due to the fact that the stretched needle thread in the rotating hook goes forward too. The thread behavior therfore is abnormal. In this case, it is supposed that if the lack of the length of the needle thread can not be compensated by the movement of the thread takeup spring and by its elongation, the thread is taken out frequently from the tention disk, and that the tightening tension is not then sufficiently generated.
In the case that Polyester or nylon threads of more elongation are used as sewing threads, the needle thread normally slips out of the rotating 'hook, i. e., first the thread slips out of the bracket and then slips out of the jib. Therefore, the behaviors of the needle thread slipped out of the rotating hook has no effect on the tightening tension.

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