Project 2 - Fluid mechanics of a toilet The objective of this project is to apply...

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Project 2 - Fluid mechanics of a toilet The objective of this project is to apply fluid mechanics principles to understand the operation and some design aspects of a toilet, as a common engineering system operating based on fluid mechanics principles (Figure 1). Basics of toilet operation Figure 1 - A toilet Figure 2 shows a schematic of a typical (so called single-trap siphonic) toilet. When the flush handle is depressed, the flush valve chain opens the flush valve (flapper) long enough for all the water in the tank to rush into the toilet bowl. All the water is then siphoned through a tube connected to the sewer and out of the bowl (Figure 3). During flushing, the float ball drops due to the lack of water in the tank, opening the inlet (fill) valve to let more water into the tank. The flush valve closes after all the water is emptied from the tank and the fresh water enters. The water level increases (from the supply line, through the inlet tube and valve, passing through the bowl refill tube, and the float ball rises. When the water reaches a certain level, this causes the inlet valve to close and stops the tank from filling further. The inlet valve must operate reliably because if it does not shut off properly, the water is wasted by keeping flowing into the tank and draining through the overflow tube into the bowl. Inlet valve Bowl refill tube Filler tube- Inlet tube- Supply line The siphon in a toilet is an upside down "U" shaped tube that connects the bowl (as a higher reservoir) to the sewer (as a lower reservoir), as shown in Figure 3. The purpose of this tube is to create low pressure on top to help empty the bowl and to transport the water in the bowl (higher reservoir) to a lower elevation. When the toilet is flushed, the water in the tank rushes quickly through the rim jet holes surrounding the bowl into the bowl. This causes the siphon tube to fill up completely, resulting in a change in pressure, that is vacuum pressure on top of the U pipe, and atmospheric pressure in the bowl. This pressure difference quickly drives the water from the bowl to the sewer. Once all the water has passed through the tube, air enters and interrupts the siphoning process (causing the gurgle sound we hear a few seconds after flushing). Then, water in the bowl is replenished when the inlet valve in the tank allows more water to come in through the supply line. float ball float arm, Handle Overflow tube Flush valve chain Tank Jet holes Flush valve Rim Bowl Figure 2 - A schematic of a toilet iriet bowl Figure 3 - Toilet bowl and siphoning through the outlet pipe outlet Answer the following questions using a toilet you have access to or by other means of obtaining real information. Note: Although the operation of a toilet is not clearly steady-state during its entire operation cycle, the aim here is to understand its operation at the initial moments of flushing the toilet and therefore, for the purpose of this project we may invoke the steady-state assumption to simplify the calculations. With this assumption, approximate numerical results can be obtained to understand the operation of the system. a) Rim jets velocity (%25): Cleaning of toilet bowl depends on the strength of the swirl motion of water inside it resulting from the velocity of the water discharged from jet holes surrounding the bowl when the toilet is flushed. To determine the jet velocity, we need to determine the flowrate out of the tank entering the bowl. First, find the volume of the flush tank; that is known from the specification of the toilets (it is often written on the toilet) or by measurement; toilets of 1.6 gallons per flush capacity are common in the US. Calculate this flowrate by measuring the time required to empty the tank (this is approximately the time from when you press the flush handle till you hear the gurgle sound). Determine the number of jet rim outlets and their diameter. Subsequently, calculate the jet velocity out of each rim hole. b) Siphon lowest pressure without losses (%25): The effectiveness of the siphoning process that empties the toilet bowl after flushing depends on the pressure on top of the U pipe. The exact shape of the siphon can often be clearly seen and measured from the side of a toilet (Figure 4). You may assume zero velocity on top of the free surface of water in the bowl as shown in Figure 3. Determine the dimensions you need from your toilet. Pay attention if the siphon pipe has the same diameter from the inlet to its highest point. If not, variation in velocity in the pipe must be taken into account. Having the flow rate through the siphon form part 1a, calculate the (vacuum) pressure at the highest point of the siphon. Neglect all losses for this part. c) Siphon lowest pressure with losses (%30): Repeat part 1b calculations but take into account all major and minor losses within the siphon pipe. Compare the results with part 1b. List clearly the junctions you considered for minor losses and their loss coefficient values. Figure 4 - Side view of a toilet Project 2 - Fluid mechanics of a toilet The objective of this project is to apply fluid mechanics principles to understand the operation and some design aspects of a toilet, as a common engineering system operating based on fluid mechanics principles (Figure 1). Basics of toilet operation Figure 1 - A toilet Figure 2 shows a schematic of a typical (so called single-trap siphonic) toilet. When the flush handle is depressed, the flush valve chain opens the flush valve (flapper) long enough for all the water in the tank to rush into the toilet bowl. All the water is then siphoned through a tube connected to the sewer and out of the bowl (Figure 3). During flushing, the float ball drops due to the lack of water in the tank, opening the inlet (fill) valve to let more water into the tank. The flush valve closes after all the water is emptied from the tank and the fresh water enters. The water level increases (from the supply line, through the inlet tube and valve, passing through the bowl refill tube, and the float ball rises. When the water reaches a certain level, this causes the inlet valve to close and stops the tank from filling further. The inlet valve must operate reliably because if it does not shut off properly, the water is wasted by keeping flowing into the tank and draining through the overflow tube into the bowl. Inlet valve Bowl refill tube Filler tube- Inlet tube- Supply line The siphon in a toilet is an upside down "U" shaped tube that connects the bowl (as a higher reservoir) to the sewer (as a lower reservoir), as shown in Figure 3. The purpose of this tube is to create low pressure on top to help empty the bowl and to transport the water in the bowl (higher reservoir) to a lower elevation. When the toilet is flushed, the water in the tank rushes quickly through the rim jet holes surrounding the bowl into the bowl. This causes the siphon tube to fill up completely, resulting in a change in pressure, that is vacuum pressure on top of the U pipe, and atmospheric pressure in the bowl. This pressure difference quickly drives the water from the bowl to the sewer. Once all the water has passed through the tube, air enters and interrupts the siphoning process (causing the gurgle sound we hear a few seconds after flushing). Then, water in the bowl is replenished when the inlet valve in the tank allows more water to come in through the supply line. float ball float arm, Handle Overflow tube Flush valve chain Tank Jet holes Flush valve Rim Bowl Figure 2 - A schematic of a toilet iriet bowl Figure 3 - Toilet bowl and siphoning through the outlet pipe outlet Answer the following questions using a toilet you have access to or by other means of obtaining real information. Note: Although the operation of a toilet is not clearly steady-state during its entire operation cycle, the aim here is to understand its operation at the initial moments of flushing the toilet and therefore, for the purpose of this project we may invoke the steady-state assumption to simplify the calculations. With this assumption, approximate numerical results can be obtained to understand the operation of the system. a) Rim jets velocity (%25): Cleaning of toilet bowl depends on the strength of the swirl motion of water inside it resulting from the velocity of the water discharged from jet holes surrounding the bowl when the toilet is flushed. To determine the jet velocity, we need to determine the flowrate out of the tank entering the bowl. First, find the volume of the flush tank; that is known from the specification of the toilets (it is often written on the toilet) or by measurement; toilets of 1.6 gallons per flush capacity are common in the US. Calculate this flowrate by measuring the time required to empty the tank (this is approximately the time from when you press the flush handle till you hear the gurgle sound). Determine the number of jet rim outlets and their diameter. Subsequently, calculate the jet velocity out of each rim hole. b) Siphon lowest pressure without losses (%25): The effectiveness of the siphoning process that empties the toilet bowl after flushing depends on the pressure on top of the U pipe. The exact shape of the siphon can often be clearly seen and measured from the side of a toilet (Figure 4). You may assume zero velocity on top of the free surface of water in the bowl as shown in Figure 3. Determine the dimensions you need from your toilet. Pay attention if the siphon pipe has the same diameter from the inlet to its highest point. If not, variation in velocity in the pipe must be taken into account. Having the flow rate through the siphon form part 1a, calculate the (vacuum) pressure at the highest point of the siphon. Neglect all losses for this part. c) Siphon lowest pressure with losses (%30): Repeat part 1b calculations but take into account all major and minor losses within the siphon pipe. Compare the results with part 1b. List clearly the junctions you considered for minor losses and their loss coefficient values. Figure 4 - Side view of a toilet