The dynamics of fluid in the elements of a pipe robot is investigated in this paper. Plane vibrations of ideal compressible fluid are analyzed by taking account the constraint of non-rotation by means of the penalty method. Reduced order numerical integration of the penalty term is performed. Graphical representation of rotations at the points of reduced integration is proposed for validation of the calculated eigenmodes. Fluid flow through different cross sections of nano-holes in metal sheets separating different compartments of a pipe robot is important in the design of a pipe robot. Calculation of the mass flow rate is necessary when performing the comparison of different cross-sections. A two-dimensional model performing the discretization of the cross-section is used for the solution of this problem. The obtained results are used in the process of design of a pipe robo