As discussed in Problem 8.52, the applied pressure difference, Δp, and corresponding volume flow

step 1 In this equation we have to find the resistance of the tube for the kerosene. So first form the

As discussed in Problem 8.52, the applied pressure...

As discussed in Problem $8.52,$ the applied pressure difference, $\Delta p,$ and corresponding volume flow rate, $Q,$ for laminar flow in a tube can be compared to the applied DC voltage $V$ across, and current $I$ through, an electrical resistor, respectively. Investigate whether or not this analogy is valid for turbulent flow by plotting the "resistance" $\Delta p / Q$ as a function of $Q$ for turbulent flow of kerosene (at $40^{\circ} \mathrm{C}$ ) in a tube $250 \mathrm{mm}$ long with inside diameter $7.5 \mathrm{mm}$.

Key Concepts

Flow Analogies to Electrical Circuits

This concept draws a parallel between fluid systems and electrical circuits, where pressure drop is analogous to voltage and volumetric flow rate is analogous to current. Though the analogy works well under conditions of laminar flow, it becomes less valid in turbulent flow due to the complex, nonlinear dynamics of turbulence.

Reynolds Number

The Reynolds number is a dimensionless quantity used to predict the flow regime in a fluid system. It indicates whether a flow will be laminar or turbulent by comparing inertial forces to viscous forces. This concept is essential in understanding why the linear analogy of hydraulic resistance to electrical resistance holds in laminar flow but fails in turbulent flow.

Turbulent Flow

Turbulent flow is characterized by chaotic fluid motion and eddy formation, which introduce nonlinearity in the relationship between pressure drop and flow rate. Unlike laminar flow, the hydraulic resistance in turbulent flow varies with the flow rate, making the simple analogy to a resistor in an electrical circuit inadequate.

Laminar Flow (Hagen-Poiseuille Law)

This concept describes the flow of a viscous fluid in a tube at conditions where the flow is smooth and orderly. Under these conditions, the pressure drop across the tube is directly proportional to the flow rate, leading to a constant hydraulic resistance analogous to Ohm’s law in electrical circuits.

Hydraulic Resistance

Hydraulic resistance is defined as the ratio of the pressure drop to the volumetric flow rate in a conduit. While this concept is straightforward under laminar flow conditions (owing to the linear relationship), it becomes complicated under turbulent conditions due to nonlinear effects and variable friction losses.

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