Am I calculating the power required and power out for a peristaltic pump correctly?

Question

I am trying to design a peristaltic pump, in a spreadsheet where I can alter the tube and casing diameter, pump RPM and some other parameters, I'm wondering if anyone can spot anything odd in this method as in some conditions it seems to give a reasonable answer, and others not (ie: Power delivered greater than power required). My process currently is:

Calculate volume per revolution:

$$V = \pi^2\cdot\left(\dfrac{\phi_{tube}}{2}\right)^2\cdot\phi_{case}$$

Calculate discharge per occlusion:

$$Q = V\cdot\dfrac{2\pi\cdot RPM}{60}$$

Calculate flow velocity:

$$v = \dfrac{Q}{A_{pipe}}$$

Calculate Reynolds number (where $\nu$ is the dynamic viscosity):

$$Re = v\cdot\dfrac{\phi_{tube}}{\nu_{water}}$$

Calculate flow friction coefficient using Nikuradse’s experimental equation:

$$f = 0.0008 + \dfrac{0.05525}{Re^{0.237}}$$

Calculate flow frictional head loss using Darcy Weisbach equation:

$$H_l = \dfrac{f\cdot\ell_{pipe}\cdot v^2}{2 \cdot 9.81 \cdot \phi_{tube}}$$

Calculate torque required (where $\mu$ is the coefficient of friction):

$$\begin{align} T =& (\mu_{roller} \cdot \text{tube re-expansion force} \cdot \phi_{i,tube}) + {}\\&(\mu_{roller} \cdot \text{tube re-expansion force} \cdot r_{crank\ shaft}) \end{align}$$

Calculate power required to drive pump:

$$P = T \cdot \dfrac{2 \cdot \pi \cdot RPM}{60}$$

Calculate total head loss assuming both ends open to atmosphere, using Bernoulli's equation:

$$H_t = \dfrac{v^2}{2g} + H_l$$

Calculate total power out (wher $\rho$ is the density):

$$P_t = \rho_{water} \cdot Q \cdot H_t \cdot 9.81$$

Seems to agree with similar projects to mine, but I get some odd results. Anyone got any ideas?

Answer 1

Here is a simple check.

power is always the product of a flow variable (current, flow rate, RPM) and an effort variable (voltage, pressure, torque).

You can measure the voltage and current going into the motor that runs the pump. This tells you how much input power is being dissipated in the motor.

Multiply this by the motor efficiency to get the net power being delivered to the pump mechanism. Ordinary electric motors are about 85% to 90% efficient.

Equate this to the mass flow rate times the pressure developed by the pump (this is the "hydraulic horsepower").

The difference between the power output of the pump and its power input tells you the efficiency of the peristaltic pump itself.