A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration \( a \) along a fixed inclined plane with angle \( \theta = 45^{\circ} \). \( P_{1} \) and \( P_{2} \) are pressures at points \( 1 \) and \( 2 \), respectively located at the base of the tube. Let \( \beta = (P_{1} - P_{2}) / (\rho g d) \), where \( \rho \) is density of water, \( d \) is the inner diameter of the tube and \( g \) is the acceleration due to gravity. Which of the following statement(s) is(are) correct?
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