Water flows through a hose that has a diameter of 0.25 in. The water has a velocity of 14.51ft/s. Find how. many gallons of water will discharge in 30 minutes.

Question

Water flows through a hose that has a diameter of 0.25 in. The water has a velocity of 14.51ft/s. Find how. many gallons of water will discharge in 30 minutes.

Answer 1

To find the volume of water discharged in 30 minutes, we first need to calculate the cross-sectional area of the hose and then multiply it by the velocity to get the discharge rate. Then, we can multiply the discharge rate by the time to get the total volume discharged. Here's how you can do it:

1. Calculate Cross-Sectional Area of the Hose: The diameter of the hose is given as 0.25 inches. We first need to convert it to feet because the velocity is given in feet per second. Since 1 foot = 12 inches, we have: Diameter=0.25 inchesDiameter=0.25 inches Radius=Diameter2=0.252=0.125 inchesRadius=2Diameter​=20.25​=0.125 inches Radius in feet=0.12512 feetRadius in feet=120.125​ feet Cross-Sectional Area=×(Radius in feet)2Cross-Sectional Area=π×(Radius in feet)2
2. Calculate Discharge Rate: The discharge rate can be calculated by multiplying the cross-sectional area by the velocity: Discharge Rate=Cross-Sectional Area×VelocityDischarge Rate=Cross-Sectional Area×Velocity
3. Calculate Total Volume Discharged in 30 minutes: Since the velocity is given in feet per second, we need to convert 30 minutes to seconds: Time=30 minutes×60 seconds/minuteTime=30 minutes×60 seconds/minute Then, we multiply the discharge rate by the time: Volume=Discharge Rate×TimeVolume=Discharge Rate×Time

Let's calculate it step by step:

1. Cross-Sectional Area: Radius in feet=0.12512=0.01041667 feetRadius in feet=120.125​=0.01041667 feet Cross-Sectional Area=×(0.01041667)2Cross-Sectional Area=π×(0.01041667)2
2. Discharge Rate: Discharge Rate=Cross-Sectional Area×14.51 ft/sDischarge Rate=Cross-Sectional Area×14.51 ft/s
3. Total Volume Discharged in 30 minutes: Time=30×60=1800 secondsTime=30×60=1800 seconds Volume=Discharge Rate×1800Volume=Discharge Rate×1800

Let's do the calculations.