diff --git a/dumux/freeflow/navierstokes/staggered/localresidual.hh b/dumux/freeflow/navierstokes/staggered/localresidual.hh
index b0abdc46ba886800bc9527181363bb72e0e59b7a..82c9af570224a75fd9d6d88384c07630e50e42b1 100644
--- a/dumux/freeflow/navierstokes/staggered/localresidual.hh
+++ b/dumux/freeflow/navierstokes/staggered/localresidual.hh
@@ -86,6 +86,8 @@ class NavierStokesResidualImpl<TypeTag, DiscretizationMethod::staggered>
     using FluxVariables = GetPropType<TypeTag, Properties::FluxVariables>;
     using Indices = typename GetPropType<TypeTag, Properties::ModelTraits>::Indices;
 
+    static constexpr bool normalizePressure = getPropValue<TypeTag, Properties::NormalizePressure>();
+
     using CellCenterResidual = CellCenterPrimaryVariables;
     using FaceResidual = FacePrimaryVariables;
 
@@ -192,7 +194,11 @@ public:
                 // Pressure term (needed because we incorporate pressure in terms of a surface integral).
                 // grad(p) becomes div(pI) + (p/r)*n_r in cylindrical coordinates. The second term
                 // is new with respect to Cartesian coordinates and handled below as a source term.
-                source += insideVolVars.pressure()/r;
+                const Scalar pressure =
+                    normalizePressure ? insideVolVars.pressure() - problem.initial(scvf)[Indices::pressureIdx]
+                                      : insideVolVars.pressure();
+
+                source += pressure/r;
             }
         }
 
diff --git a/test/freeflow/navierstokes/channel/pipe/params.input b/test/freeflow/navierstokes/channel/pipe/params.input
index 9bcb4dacc3c10c43bbeba8a960d68da7c40292c3..66b549898c5ff69a86d5b5125ea5f657adef2aea 100644
--- a/test/freeflow/navierstokes/channel/pipe/params.input
+++ b/test/freeflow/navierstokes/channel/pipe/params.input
@@ -9,8 +9,7 @@ Grading1 = 1
 [Problem]
 Name = test_ff_stokes_channel_pipe
 MeanInletVelocity = 0.1 # [m/s]
-
-[Problem]
+InitialPressure = 1.0e5 # [Pa]
 EnableGravity = false
 EnableInertiaTerms = false
 
diff --git a/test/freeflow/navierstokes/channel/pipe/problem.hh b/test/freeflow/navierstokes/channel/pipe/problem.hh
index 91668701cdd87676fa18c63501cc941ccc36c94d..21ed3446d619000aa3fa0012c0ab3a1f98095bb8 100644
--- a/test/freeflow/navierstokes/channel/pipe/problem.hh
+++ b/test/freeflow/navierstokes/channel/pipe/problem.hh
@@ -52,6 +52,7 @@ public:
     {
         name_ = getParamFromGroup<std::string>(this->paramGroup(), "Problem.Name");
         meanInletVelocity_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.MeanInletVelocity");
+        initialPressure_ = getParamFromGroup<Scalar>(this->paramGroup(), "Problem.InitialPressure");
         mu_ = getParam<Scalar>("Component.LiquidKinematicViscosity")*getParam<Scalar>("Component.LiquidDensity");
 
         pipeRadius_ = this->gridGeometry().bBoxMax()[0] - this->gridGeometry().bBoxMin()[0];
@@ -109,7 +110,11 @@ public:
     { return analyticalSolution(globalPos); }
 
     PrimaryVariables initialAtPos(const GlobalPosition& globalPos) const
-    { return PrimaryVariables(0.0); }
+    {
+        PrimaryVariables values(0.0);
+        values[Indices::pressureIdx] = initialPressure_;
+        return values;
+    }
 
     PrimaryVariables analyticalSolution(const GlobalPosition& globalPos) const
     {
@@ -139,6 +144,7 @@ private:
     { return globalPos[1] > this->gridGeometry().bBoxMax()[1] - eps_; }
 
     std::string name_;
+    Scalar initialPressure_;
     Scalar meanInletVelocity_;
     Scalar mu_;
     Scalar pipeRadius_, pipeLength_;