Question

Consider a device with one inlet and one outlet. If the volume flow rates at the inlet and at the outlet are the same, is the flow through this device necessarily steady? Why?

Short answer

Explain your conclusion. Answer: No, the flow through the device is not necessarily steady just because the volume flow rates at the inlet and outlet are the same. To determine if the flow is steady, other properties such as the fluid density at the inlet and outlet would need to be considered. A constant volume flow rate does not guarantee a steady flow, as the net mass flow rate through the control volume also needs to be constant over time.

Step-by-step solution

Define steady flow

A flow is considered to be steady if all fluid properties, including velocities, pressures, and densities, at every point in the flow do not change over time. Mathematically, this means that the partial derivatives for each of these properties with respect to time must be zero.

Identify the criteria for steady flow

For a flow to be steady, the net mass flow rate through a control volume must be constant. Since the mass flow rate is the product of the volume flow rate and the density, we can write this criterion as: Net mass flow rate through the control volume = (Density at inlet × Volume flow rate at inlet) - (Density at outlet × Volume flow rate at outlet) If this net mass flow rate is constant over time, the flow is steady.

Analyze the given conditions

We are given that the volume flow rate at the inlet and outlet is the same, denoted by V_inlet = V_outlet. However, we do not have any information about the densities at the inlet and outlet.

Determine if the flow is steady

Since we do not know the densities at the inlet and outlet, we cannot determine the net mass flow rate through the control volume and, therefore, cannot verify if the flow is steady. A constant volume flow rate at the inlet and outlet is not enough to guarantee a steady flow. Other properties, such as the fluid density at the inlet and outlet, would need to be considered to determine if the flow is steady. So, the answer is no, the flow through this device is not necessarily steady just because the volume flow rates at the inlet and at the outlet are the same.