A horizontal hypodermic syringe consists of a wide cylindrical barrel of cross-sectional area \(A_{\text{barrel}}\) connected to a narrow needle of cross-sectional area \(A_{\text{needle}}\), where \(A_{\text{barrel}} > A_{\text{needle}}\). An ideal, incompressible fluid completely fills the syringe. A plunger is pushed to move fluid through the barrel at a constant speed \(v_{\text{barrel}}\), ejecting it horizontally through the open needle into the atmosphere at pressure \(P_{\text{atm}}\). Which of the following correctly compares the fluid speed in the needle \(v_{\text{needle}}\) to \(v_{\text{barrel}}\), and the absolute fluid pressure in the barrel \(P_{\text{barrel}}\) to \(P_{\text{atm}}\)?