In a laminar, incompressible, fully-developed pipe flow of a Newtonian fluid, as shown in the figure, the velocity profile over a cross-section is given by \( u = U \left( 1 - \frac{r^2}{R^2} \right) \), where \( U \) is a constant. The pipe length is \( L \) and the fluid viscosity is \( \mu \). The power \( P \) required to sustain the flow is expressed as \( P = c \mu L U^2 \), where \( c \) is a dimensionless constant. The value of the constant \( c \) (up to one decimal place) is \(\underline{\hspace{1cm}}\).
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