# Velocity Field#

 $$v_r$$ 1 v_r $$v_\theta$$ 2 v_theta $$v_\phi$$ 3 v_phi $$v_r'$$ 4 vp_r $$v_\theta'$$ 5 vp_theta $$v_\phi'$$ 6 vp_phi $$\overline{v_r}$$ 7 vm_r $$\overline{v_\theta}$$ 8 vm_theta $$\overline{v_\phi}$$ 9 vm_phi $$\frac{\partial v_r}{\partial r}$$ 10 dv_r_dr $$\frac{\partial v_\theta}{\partial r}$$ 11 dv_theta_dr $$\frac{\partial v_\phi}{\partial r}$$ 12 dv_phi_dr $$\frac{\partial v_r'}{\partial r}$$ 13 dvp_r_dr $$\frac{\partial v_\theta'}{\partial r}$$ 14 dvp_theta_dr $$\frac{\partial v_\phi'}{\partial r}$$ 15 dvp_phi_dr $$\frac{\partial \overline{v_r}}{\partial r}$$ 16 dvm_r_dr $$\frac{\partial \overline{v_\theta}}{\partial r}$$ 17 dvm_theta_dr $$\frac{\partial \overline{v_\phi}}{\partial r}$$ 18 dvm_phi_dr $$\frac{\partial v_r}{\partial \theta}$$ 19 dv_r_dt $$\frac{\partial v_\theta}{\partial \theta}$$ 20 dv_theta_dt $$\frac{\partial v_\phi}{\partial \theta}$$ 21 dv_phi_dt $$\frac{\partial v_r'}{\partial \theta}$$ 22 dvp_r_dt $$\frac{\partial v_\theta'}{\partial \theta}$$ 23 dvp_theta_dt $$\frac{\partial v_\phi'}{\partial \theta}$$ 24 dvp_phi_dt $$\frac{\partial \overline{v_r}}{\partial \theta}$$ 25 dvm_r_dt $$\frac{\partial \overline{v_\theta}}{\partial \theta}$$ 26 dvm_theta_dt $$\frac{\partial \overline{v_\phi}}{\partial \theta}$$ 27 dvm_phi_dt $$\frac{\partial v_r}{\partial \phi}$$ 28 dv_r_dp $$\frac{\partial v_\theta}{\partial \phi}$$ 29 dv_theta_dp $$\frac{\partial v_\phi}{\partial \phi}$$ 30 dv_phi_dp $$\frac{\partial v_r'}{\partial \phi}$$ 31 dvp_r_dp $$\frac{\partial v_\theta'}{\partial \phi}$$ 32 dvp_theta_dp $$\frac{\partial v_\phi'}{\partial \phi}$$ 33 dvp_phi_dp $$\frac{\partial \overline{v_r}}{\partial \phi}$$ 34 dvm_r_dp $$\frac{\partial \overline{v_\theta}}{\partial \phi}$$ 35 dvm_theta_dp $$\frac{\partial \overline{v_\phi}}{\partial \phi}$$ 36 dvm_phi_dp $$\frac{1}{r}\frac{\partial v_r}{\partial \theta}$$ 37 dv_r_dtr $$\frac{1}{r}\frac{\partial v_\theta}{\partial \theta}$$ 38 dv_theta_dtr $$\frac{1}{r}\frac{\partial v_\phi}{\partial \theta}$$ 39 dv_phi_dtr $$\frac{1}{r}\frac{\partial v_r'}{\partial \theta}$$ 40 dvp_r_dtr $$\frac{1}{r}\frac{\partial v_r'}{\partial \theta}$$ 41 dvp_theta_dtr $$\frac{1}{r}\frac{\partial v_r'}{\partial \theta}$$ 42 dvp_phi_dtr $$\frac{1}{r}\frac{\partial \overline{v_r}}{\partial \theta}$$ 43 dvm_r_dtr $$\frac{1}{r}\frac{\partial \overline{v_\theta}}{\partial \theta}$$ 44 dvm_theta_dtr $$\frac{1}{r}\frac{\partial \overline{v_\phi}}{\partial \theta}$$ 45 dvm_phi_dtr $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_r}{\partial \phi}$$ 46 dv_r_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\theta}{\partial \phi}$$ 47 dv_theta_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\phi}{\partial \phi}$$ 48 dv_phi_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_r'}{\partial \phi}$$ 49 dvp_r_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\theta'}{\partial \phi}$$ 50 dvp_theta_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\phi'}{\partial \phi}$$ 51 dvp_phi_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_r}}{\partial \phi}$$ 52 dvm_r_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_\theta}}{\partial \phi}$$ 53 dvm_theta_dprs $$\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_\phi}}{\partial \phi}$$ 54 dvm_phi_dprs $$\frac{\partial^2 v_r}{\partial r^2}$$ 55 dv_r_d2r $$\frac{\partial^2 v_\theta}{\partial r^2}$$ 56 dv_theta_d2r $$\frac{\partial^2 v_\phi}{\partial r^2}$$ 57 dv_phi_d2r $$\frac{\partial^2 v_r'}{\partial r^2}$$ 58 dvp_r_d2r $$\frac{\partial^2 v_\theta'}{\partial r^2}$$ 59 dvp_theta_d2r $$\frac{\partial^2 v_\phi'}{\partial r^2}$$ 60 dvp_phi_d2r $$\frac{\partial^2 \overline{v_r}}{\partial r^2}$$ 61 dvm_r_d2r $$\frac{\partial^2 \overline{v_\theta}}{\partial r^2}$$ 62 dvm_theta_d2r $$\frac{\partial^2 \overline{v_\phi}}{\partial r^2}$$ 63 dvm_phi_d2r $$\frac{\partial^2 v_r}{\partial \theta^2}$$ 64 dv_r_d2t $$\frac{\partial^2 v_\theta}{\partial \theta^2}$$ 65 dv_theta_d2t $$\frac{\partial^2 v_\phi}{\partial \theta^2}$$ 66 dv_phi_d2t $$\frac{\partial^2 v_r'}{\partial \theta^2}$$ 67 dvp_r_d2t $$\frac{\partial^2 v_\theta'}{\partial \theta^2}$$ 68 dvp_theta_d2t $$\frac{\partial^2 v_\phi'}{\partial \theta^2}$$ 69 dvp_phi_d2t $$\frac{\partial^2 \overline{v_r}}{\partial \theta^2}$$ 70 dvm_r_d2t $$\frac{\partial^2 \overline{v_\theta}}{\partial \theta^2}$$ 71 dvm_theta_d2t $$\frac{\partial^2 \overline{v_\phi}}{\partial \theta^2}$$ 72 dvm_phi_d2t $$\frac{\partial^2 v_r}{\partial \phi^2}$$ 73 dv_r_d2p $$\frac{\partial^2 v_\theta}{\partial \phi^2}$$ 74 dv_theta_d2p $$\frac{\partial^2 v_\phi}{\partial \phi^2}$$ 75 dv_phi_d2p $$\frac{\partial^2 v_r'}{\partial \phi^2}$$ 76 dvp_r_d2p $$\frac{\partial^2 v_\theta'}{\partial \phi^2}$$ 77 dvp_theta_d2p $$\frac{\partial^2 v_\phi'}{\partial \phi^2}$$ 78 dvp_phi_d2p $$\frac{\partial^2 \overline{v_r}}{\partial \phi^2}$$ 79 dvm_r_d2p $$\frac{\partial^2 \overline{v_\theta}}{\partial \phi^2}$$ 80 dvm_theta_d2p $$\frac{\partial^2 \overline{v_\phi}}{\partial \phi^2}$$ 81 dvm_phi_d2p $$\frac{\partial^2 v_r}{\partial r \partial \theta}$$ 82 dv_r_d2rt $$\frac{\partial^2 v_\theta}{\partial r \partial \theta}$$ 83 dv_theta_d2rt $$\frac{\partial^2 v_\phi}{\partial r \partial \theta}$$ 84 dv_phi_d2rt $$\frac{\partial^2 v_r'}{\partial r \partial \theta}$$ 85 dvp_r_d2rt $$\frac{\partial^2 v_\theta'}{\partial r \partial \theta}$$ 86 dvp_theta_d2rt $$\frac{\partial^2 v_\phi'}{\partial r \partial \theta}$$ 87 dvp_phi_d2rt $$\frac{\partial^2 \overline{v_r}}{\partial r \partial \theta}$$ 88 dvm_r_d2rt $$\frac{\partial^2 \overline{v_\theta}}{\partial r \partial \theta}$$ 89 dvm_theta_d2rt $$\frac{\partial^2 \overline{v_\phi}}{\partial r \partial \theta}$$ 90 dvm_phi_d2rt $$\frac{\partial^2 v_r}{\partial r \partial \phi}$$ 91 dv_r_d2rp $$\frac{\partial^2 v_\theta}{\partial r \partial \phi}$$ 92 dv_theta_d2rp $$\frac{\partial^2 v_\phi}{\partial r \partial \phi}$$ 93 dv_phi_d2rp $$\frac{\partial^2 v_r'}{\partial r \partial \phi}$$ 94 dvp_r_d2rp $$\frac{\partial^2 v_\theta'}{\partial r \partial \phi}$$ 95 dvp_theta_d2rp $$\frac{\partial^2 v_\phi'}{\partial r \partial \phi}$$ 96 dvp_phi_d2rp $$\frac{\partial^2 \overline{v_r}}{\partial r \partial \phi}$$ 97 dvm_r_d2rp $$\frac{\partial^2 \overline{v_\theta}}{\partial r \partial \phi}$$ 98 dvm_theta_d2rp $$\frac{\partial^2 \overline{v_\phi}}{\partial r \partial \phi}$$ 99 dvm_phi_d2rp $$\frac{\partial^2 v_r}{\partial \theta \partial \phi}$$ 100 dv_r_d2tp $$\frac{\partial^2 v_\theta}{\partial \theta \partial \phi}$$ 101 dv_theta_d2tp $$\frac{\partial^2 v_\phi}{\partial \theta \partial \phi}$$ 102 dv_phi_d2tp $$\frac{\partial^2 v_r'}{\partial \theta \partial \phi}$$ 103 dvp_r_d2tp $$\frac{\partial^2 v_\theta'}{\partial \theta \partial \phi}$$ 104 dvp_theta_d2tp $$\frac{\partial^2 v_\phi'}{\partial \theta \partial \phi}$$ 105 dvp_phi_d2tp $$\frac{\partial^2 \overline{v_r}}{\partial \theta \partial \phi}$$ 106 dvm_r_d2tp $$\frac{\partial^2 \overline{v_\theta}}{\partial \theta \partial \phi}$$ 107 dvm_theta_d2tp $$\frac{\partial^2 \overline{v_\phi}}{\partial \theta \partial \phi}$$ 108 dvm_phi_d2tp