Tub/Shower Head: Fluid dynamics question

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A shower head was installed in a bathtub but initially provided inadequate water flow due to a small orifice size of 3/32". After enlarging the orifice to 3/16", the flow rate significantly improved, satisfying the customer. The flow rate increases quadratically with the diameter of the orifice, meaning that doubling the diameter can quadruple the flow rate. It's important to consider municipal building codes that may require flow restrictors in shower heads to ensure compliance. Always inform customers about these regulations before making modifications.
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I installed a shower head in a customer's bath tub last week. The customer was not happy with the flow of water coming from the shower--so I removed the shower head and noted the orfice that leads to the spray area in the shower head was only 3/32" in diameter. I drilled a hole enlarging the orfice to 3/16". I reinstalled the shower head and the customer was happy with the new larger volume of water.

Water pressure is at 25psi and enters the shower head via a 1/2" steel pipe and then from the orfice fills a standard shower head to spray out.

How can I calculate the volume differences with changes in orfice size?

Thank you
Josh
 
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The relevant quantity is flow rate: volume/time.

This scales quadratically along with the diameter of the hole, so doubling the diameter quadrupled the flow rate.
 
Some municipal building codes require flow restrictors in replacement shower heads, just as they require low flush toilets. You should check the code so you don't unkowingly put your customer out of compliance. (They can always choose to do it anyway, once they're informed ;o)
 

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