Consider unsteady flow in the constant diameter, horizontal pipe shown in Fig. P5.67. The velocity is uniform throughout the entire pipe, but it is a function of time: \(\mathbf{V}=u(t) \hat{\mathbf{i}}\). Use the \(x\) component of the unsteady momentum equation to determine the pressure difference \(p_{1}-p_{2}\). Discuss how this result is related to \(F_{x}=m a_{x}\).

Figure P5.67

u (t) (1) p = density (2)