Help with Mass Flow Rate

Question

I'm a beginner in chemical engineering so apologies in advance if this question is very basic!

The Problem

You are required to measure the mass and volumetric flow rate of a slurry stream. The slurry contains only water and solids. You take a bucket and stop watch and measure the time taken to fill the bucket. From these measurements, the following information is obtained.

• The stream fills a 10 litre bucket in 13.5s.

• A sample of the slurry weighing 767g is filtered and dried. The dry solids weigh 148g. 􏰀

• The density of the solids only is known to be 3200kg/m³.

  TASK: Calculate the mass flow rate of the slurry stream.

My Attempt

1. I converted the rate at which the slurry filled the bucket to m³/s.

10L / 13.5s = 0.01m³/13.5s = 0.000741 m³/s

2. I calculated the density of the slurry by adding together the relative densities of its dry solids and its water.

density of slurry = (ratio of dry solids:slurry stream)(density of dry solids) + (ratio of water:slurry stream)(density of water) =(0.148/0.767)(3200 kg/m³) + (0.619/0.767)(1000kg/m³) = (0.193)(3200 kg/m³) + (0.807)(1000 kg/m³) = 1424.6 kg/m³

3. I plugged in the respective values into the equation mass flow rate = density * volumetric flow rate.

mass flow rate = 1424.6 kg/m³ * 0.000741 m³/s = 1.055 kg/s

Correct Answer

According to the answer key, the answer is supposed to be 0.854 kg/s.

I'm not sure where I went wrong.

Answer 1

It's the density calculation you have. You're almost there! This site explains it pretty well:

https://www.engineeringtoolbox.com/slurry-density-calculate-d_1188.html

Density of slurry=1/[(ratio of solid/mixture masses)/(solid density)+(ratio of liquid/mixture masses)/(liquid density)]

Density of slurry=1/[0.148 kg/0.767 kg /(3200 kg/m^3) +0.619 kg/0.767 kg/(1000 kg/m^3)]

I hope this makes some sense!