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Chapter 9: Problem 35

Two different fluids flow over two identical flat plates with the same laminar free-stream velocity. Both fluids have the same viscosity, but one is twice as dense as the other. What is the relationship between the drag forces for these two plates?

Short Answer

Expert verified
The drag force experienced by the plate with the denser fluid (fluid B) is twice the drag force experienced by the plate in contact with the less dense fluid (fluid A). Thus, the relationship between the drag forces for these two plates is \(F_{dB} = 2 \times F_{dA}\).

Step by step solution

01

Understand the given

We know that two fluids A and B have identical viscosity andthey flow over two identical flat plates. But fluid B is twice as dense as fluid A. We need to find the relationship between drag forces experienced by these plates.
02

Calculation of drag forces for both fluids

As per the drag force equation \(F_d = 0.5 \times \rho \times U \times A \times C_d\), we know that both fluids have the same viscosity, so they will experience the same drag coefficient \(C_d\). We also know that the other terms (U, A) are same for both fluids, except the density (\(\rho\)). Therefore, for fluid A with density \(\rho\), the drag force \(F_{dA}\) will be \(0.5 \times \rho \times U\times A \times C_d\), and for fluid B with density \(2\rho\), the drag force \(F_{dB}\) will be \(0.5 \times (2\rho) \times U\times A \times C_d\).
03

Establishing the relationship between the drag forces

Comparing the equations for \(F_{dA}\) and \(F_{dB}\), we find that the drag force \(F_{dB}\) experienced by the plate in contact with fluid B is double the drag force \(F_{dA}\) experienced by the plate in contact with fluid A. Hence, \(F_{dB} = 2 \times F_{dA}\), which is the relationship between the drag forces for these two plates.

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