What is the mass flux through a kidney?

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In summary, the rate of change of mass of water in the kidney is 3.99*10^-4 kg/s. The error in the original solution was due to using incorrect values for the inflow and outflow fluxes.
  • #1
giacomh
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Homework Statement



Water enters a kidney through a tube at 10 mL/min. It exits through a 6-mm-diameter tube at 20 mm/s.What is the rate of change of mass of water in the kidney?

Homework Equations



m=vpa
q=va

After conversions to meters
V=.02
Q=.000167
A=(pi/4)*.006^2 = .0000282

The Attempt at a Solution



dm/dt-Qp+VAp=0
dm/dt-(.000167)(999.1)+(.0000282)(.02)(999.1)=0
dm/dt=.165 kg/s

Needless to say, that's not the right answer, but I can't figure out where I went wrong.
 
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  • #2
You are incorrectly finding the positive flux. It is 1.67*10^-4 for the inflow and 5.655*10^-4 for the outflow.

Inflow 10 mL/min * (min/60 s) * (1 cm^3/mL) * (m^3/1000000 cm^3) = 1.67*10^-7 m^3/s

Outflow=V*A { 20 mm/s * (m/1000mm) } * { [(6 mm/2)/1000]^2 * pi } = 5.65*10^-7 m^3/s

Δm = -density*Q(in) + density*Q(out)
= [-1000*.000000167]+[1000*.000000565]
= 3.99*10^-4 kg/s
 

1. What is mass flux and how does it relate to the kidney?

Mass flux is the rate at which a substance is transported through a given area. In the context of the kidney, mass flux refers to the movement of substances (such as water and solutes) through the kidney's filtration system. This process is essential for maintaining the body's fluid balance and removing waste products from the blood.

2. What factors influence mass flux through the kidney?

There are several factors that can affect mass flux through the kidney, including blood pressure, hormone levels, and the health of the kidney itself. Specifically, changes in blood pressure can impact the rate of filtration, while hormones like aldosterone and antidiuretic hormone can alter the kidney's ability to reabsorb water and electrolytes.

3. How is mass flux measured in the kidney?

Mass flux through the kidney can be measured using various techniques, but one common method is through the use of clearance tests. These tests involve measuring the concentration of a substance (such as creatinine or inulin) in the blood and urine, and using this data to calculate the rate of filtration through the kidney.

4. What is the significance of mass flux through the kidney?

The kidney plays a crucial role in maintaining the body's homeostasis by regulating the volume and composition of bodily fluids. Mass flux through the kidney is essential for this function, as it helps to remove waste products and excess fluid from the body while also maintaining a balance of essential substances like electrolytes and hormones.

5. How does disease or dysfunction of the kidney affect mass flux?

Disease or dysfunction of the kidney can significantly impact mass flux through this organ. For example, conditions like kidney failure or kidney disease can impair the kidney's ability to filter and reabsorb substances, leading to imbalances in the body's fluid and electrolyte levels. Additionally, high blood pressure or diabetes can also affect the kidney's function and ultimately impact mass flux through this organ.

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